Dru's Story

....Yeah.... that was her backstory... which the other's also had, before they had different stories in the present that built on that, that took their character in new directions..... Which is the point I was getting at with Dru, who did not have the latter.

I don't think it would preclude that at all.  I mean, for one thing, her mental illness could be attributed, at least in part, in her becoming the sort of unholy creature she abhorred; after losing her loved ones to such a creature and preparing to take her holy vows.  So there's arguably some degree of conflict built into her psyche as to her innate desire to be good or bad; and invariably the latter wins out for want of a soul.  Plus, how "sane" is an evil vampire to begin with; especially if the conceit is that without a soul they lack the capacity to every truly be good? 
In general though, I don't think a mental illness necessarily excludes the possibility of overcoming that illness or making positive change in spite of it.  

I've often argued that something similar is going on with the whole Angel vs. Angelus thing.  Liam was someone who, in life wanted nothing more than his father's approval, but always came up short in every estimation; and even in his own words in arguing with his father, the closest he'd ever felt like he ever lived up to his expectations was in being the failure and disappointment he believed his father thought him to be.  All he wanted was his father's acceptance and approval and deep down he invariably figured one day he would achieve that, at which point he would put his drinking and debauchery behind him and live a life worth living.  Being turned into a vampire changed that, it was a consequence too far that he couldn't take back; with this change he could never be accepted by his father or by God, and for anything else about his life up to that point (...of his death) this broke his own psyche.  He couldn't accept that this was what he was now and acts out in ways that are either intended to erase any reminder of what he was, or will almost certainly lead to enough people who want him dead that they'll put him out of his misery.  We regularly see how unnerved he is by any lingering  reminder of his humanity, while other vampires have no such issue; to the point that he's willing to have the world sucked into literal hell, with him along with it.  When he talks about awakening Acathla and that "it will all being over," he sounds more like someone seeking his own release.

Much the same could be said of Dru; she's right there with Angel when planning to awaken Acathla. Anyone with an ounce of self-preservation would know that's a bad idea, even if you are evil.  It could a matter of something or someone giving her a sense of clarity or purpose; for that matter I even thought it might be worth exploring the fact that if you drive an evil being insane, might they, in their irrational behavior, behave good?  

Another possibility that through the confluence of her circumstances, either on the cusp of taking her holy vows or having just become a nun after already being, as Angel noted when he first saw her, as someone so "pure," someone with a connection to higher powers through vision who is subsequently consecrated and immediately turned into a vampire - what if as a result she never lost her soul; and that's why she's insane?  She's immediately and eternally caught in the middle, the good and the evil both whispering in her ear; and to cope she just checks out and does whatever her companions want to do, rather than make a choice of her own.  Tear a bloody swath across Europe?  Okay.  Sire a mate? Okay.  She copes by identifying her abuses as her mummy and daddy; yet where William/Spike would in that sense be her son, he typically calls the shots when they're seen together before his character evolves.  
When Angel and Spike are re-ensouled, especially Spike, they're initial response and behavior is not unlike Dru's; only they eventually work past it. 

As for her visions as a vampire, most, if not all of them aren't inherently evil predictions, but rather facts of what is or what will be; and it's "how" that knowledge is acted upon that determines the positive of negative impact on the world around them.  I've recently been contemplating this concept in regards to Cordelia's visions and the idea of a higher power sending them to her for a some great, intentional plan; and that Angel was charged with being a champion of the light.  It all kind of stemmed from watching "I will remember you" again recently and thinking about the Oracles saying Angel was released from his duties as champion; and thinking, "....what?"  Angel was drafted to be a force Good, at least not before coming to LA or even after, but before he met Doyle.  He was doing it because it was right and because he chose to do good; and even if he weren't a vampire, he could still choose to fight the good fight, no less than Cordelia, Gunn, Wesley or Fred would do.  The visions are better defined as knowledge of events where Angel and those who fight with him have the greatest potential to effect a positive outcome, but that the choice, as always, is their to determine whether to act and attempt to effect that change, or let the alternative come to pass; and it's the decision to do good that makes them champions and not the other way around.  
So for Dru and her visions, what she sees isn't inherently good or bad, but how she or others she associates with responds to the knowledge she gains is.  Knowing that Acathla was in Sunnydale or that Jenny was trying to re-ensoul Angel wasn't inherently a bad visions, it was just a fact; and in the hands of someone who decides to do good with that knowledge would have responded to it in completely different ways.  In which case what she would need in order to do good those visions is a catalyst in that direction.

He does want his approval, desperately; Darla even observes this shortly after Angel's been turned and had just killed his father - she notes how the one thing Liam/Angel clearly wanted was his father's approval, which now that he's killed him he'll never get.  Angelus tries to dismiss this, but it seems clear to me in the fights between Liam and his dad and the passion behind both men that neither are indifferent to each other; and Liam makes a similar comparison that his father should be happy, because he's living up to his expectations of him as a failure.  And the real, beautiful tragedy of this story between Angel and his father is that scene during Liam's funeral and the look on his father's face, of a man who's just barely keeping it together, because he has to be stoic in front of all these people, but then he stays at his son's grave long after they've left.  And the tragic aspect is that Liam never knows; he never finds out what he truly meant to his father.

I would say with Dru, they keep it rather ambiguous at what point exactly her mind broke; in part because they didn't quite dive as fully into her history as the other three.  There's good chunks that are known, but they skip a lot; especially what her state of mind was when she was turned.  Ostensibly if she was turned on the day she took her holy orders, she was reasonably sane up to that point, other would the church have allowed her to become a nun?  That's why I think it tracks that it was the act of turning her into the very sort of creature that had been tormenting her and at odds with her pious life that finally broke her.
But they also use the idea of her being "insane" in that kind of cliched, nebulous sort of way; there's a reason now that such defense pleas are "by reason of mental defect," as the mental sciences are far more nuanced.  And even then, being found not guilty by reason of mental defect or instability wouldn't mean they would just walk free; it generally would mean they would go to a psychiatric hospital for treatment, until such a time, if any, that the underlying cause of that defect or instability was resolved and that person were no longer a threat to society. 
However you slice it, it is a mental illness, because there is distinctly something wrong with her mind.  At the very least, there's arguably some degree of post-traumaric stress at play; maybe some Stockholm syndrome, since she ultimately identified with those who tormented her for so long.  It's probably not just one thing, but a combination of mental issues, all stemming from her abuse and mental tortures enacted on her by Angelus, but it's also quite possible that just the nature of what she's become and it being completely antithetical to anything she would have ever wanted to be is another factor and the final, ultimate humiliation by Angelus, turning her into one of the very monsters she fears, forever.
True, but that's true of all vampires; even those with a sole note how there's still a compulsion for the monster inside them wanting to cause chaos, thirsting for blood and hungry just to kill anything.
Her dynamic with Angel and Spike I think is a little more nuanced; and I might argue that she was taking her cue more from Angel, who clearly enjoyed getting a rise out of Spike and using Dru to do it.  When Dru showed Spike affection (Spike laying it on with Dru), Angel never reacted the way Spike did when the roles were reversed and either Angel or Dru toyed with the other; and it was more often Angel who was the overt aggressor, at least in the encounters we were shown.  This could arguably be pointed to as another example of Dru having been completely broken down mentally and now identifying with her abuser; and any attention he gives her validates her disassociate perspective on the type of relationship she has with Angel.  Even before she sires William, she's laments that Angel won't do anything with her, even though she comes to see him as her new "daddy".  Even Darla gives the okay for this, but it's not until Spike's in the picture, and after he and Angel have buddied up and William  confides in him that he and Dru have some sort of eternal love that Angel actually screws Drusilla and Spike walks in on them - presumably planned for just such an effect on Angel's part.  The same is true once they're in Sunnydale; even when Angel has a soul, he uses that connection with Dru, knowing that it'll get under Spike's skin and it continues after Angel loses his soul and teams up Dru and Spike.

As for the redemption and what Dru knew when and what she has control over, there's a difference between guilt and culpability.  Even if she wasn't in her right mind and everything she did and if a court of law would find her "innocent" on those grounds if she were suddenly clear minded and no longer a vampire or re-ensouled, she would still remember doing those things and feel responsible for those actions, no less than Angel, Spike or Darla did; and arguably the circumstances are more or less the same.  For one thing, the show's contention was often that when a human is turned into a vampire, the human is gone and a demon is simply walking around in their body; which should mean that none of these humans who were turned were ever actually guilty, because they weren't really there, it was just something that looked and sounded like. And I guess restoring their soul essentially means returning the true person to their body, even while it's still trapped inside with the demon.

I've never really bought into this, because even though they say that's how it is, there's clearly a continuation of consciousness and mentality from one moment to the next; the difference between life and post-life is a change of form, the hybridization of the human and the demon, with the mind mostly intact.  They experience it as a single, contiguous existence and the vampire conceptualizes everything from before they became a vampire from the first person perspective.  It wasn't "William's" mom that the vampire that would one day be known as Spike would sire then dust, it was his mom.  Dru remarks how Angel had killed her uncle, Angel admits that he killed his own father.  And when Spike and Angel are re-ensouled, they have no concept of having been anywhere else; the soul isn't their consciousness or life essence or memories.  There's confusion, but everything they did before and after is the same entity, just with an altered outlook.

But there's the rub in terms of culpability verse guilt; because by all account, just by virtue of not having a soul, a vampire is not supposed to be able to be good.  That's why Angel could be trusted, but Angelus couldn't be; why Buffy could never love Spike and why his getting a soul meant he could have his chip removed and help fight the First.  Whatever that soul is, it presents a capacity for behavior that vampires don't have without it; so is it any different from some like Drusilla having a mental breakdown committing a heinous act, only to have her rationality restored?

Mind you, the two shows' approach to what the soul was supposed to be was inconsistent and ultimately undermined Spike's growth over the course of season 4 and 5 and early season 6.  This is someone who legitimately was able to love - and I say that as someone who isn't a fan of Buffy and Spike; I do believe he legitimately loved her.  It wasn't always a healthy love, and I'm not convinced it was reciprocated.  More than that, he had the capacity to care for and respect Joyce and to want to protect Dawn.  He tried to help Dawn bring Joyce back, he was going to anonymously leave flowers at the house; and he was willing to have the shit beat him out of him by Glory and still protect the secret that Dawn was the Key.  And then his reaction Buffy's death was magnificent.  I almost hate it by virtue of it overshadowing the reactions of the other characters who deserve to mourn her that powerfully, but it's too wonderful. Then to compound that by having him staying true to his word and protect Dawn after Buffy's death, and to know that he'd been counting the days since she died and replaying the moment in his head - fucking spectacular.  That has real meat to it; this is a character with the capacity to make a choice to be good and then doing it.  Even when he'd rather play with the biker demons and revel in the carnage and chaos, he chooses the path of greater resistance by staying with Dawn and making sure she's safe.
And then they flush it all away with the toxic "relationship" between Spike and Buffy throughout season 6; then having him assault her, all to prove that he's still really a monster - but oh, wait, he's able to recognize that what he did was wrong and proactively decides to atone by fighting for and earning a soul, that will allow him to do all the things he was already sort of doing.....
The best that I've been able to work out is that the soul is essentially the Superego of a person's psyche; leaving behind the ID (impulse) and Ego (Personality).  The latter two work primarily on the pain/pleasure principal, whereas the Superego keeps those areas in check and applies concepts of morality and conscience.

I think the refutation of that lies in the fact that the same goes for the likes of Spike and Darla.  Spike was meant to die when the church collapsed after trying to bring Dru back to full health, but everyone liked what he was doing so much that they kept him around and kept his story going.
Meanwhile, Darla gets staked in episode 7, yet a lot of her character gets built in flashback; and we're all the better for it, considering how little depth the character was given prior to the episode "Angel."  Even just the depiction of her in her heyday as an evil vampire, siring Angel and cutting a bloody swath across the globe added a rich substance to her character that was sorely lacking beforehand.  Then they double down and bring her back, as human no less, and explore that and her dying again, and the effect it has on Angel; plus her being the source of his perfect despair, his epiphany, then the whole arc of her being pregnant with Connor....  Who would ever have seen that coming from the Master's toady as depicted in "Welcome to the Hellmouth"?

But that's also what's so great about watching shows like Buffy or Angel; when they're able to take what starts off as a minor role and they turn it into something so much more.  I mean look at what they did with Jonathan, Harmony, Lindsey, Lorne, Amy, Wesley.  I've lost count how many times I've watch both Angel or Buffy, and I'm in the midst of yet another re-watch; and the other day I marveled at how adept the writers were for being able to introduce someone who almost instantly becomes a main character as if it were a foregone conclusion that this person has to be part of this show.  There aren't a lot of shows that can do that; the ones that could and did it effectively are iconic, but a lot of show have also failed spectacularly when trying to add a character or reinvent itself that way. 
Both shows did it well, but I think Angel did it more effectively, as evidence by how dynamic their main cast was over the course of their 5 seasons; and their willingness to take greater chances with their characters.

This is why I would probably fail a lot of those types of classes; as you can see, I like to speculate.  I got admonished by a teacher for an online course I was trying out years ago for writing too much; and was advised that I would start losing points in the future if they weren't shorter.  My response was I was going to have to settle for losing points, because I wasn't going to write less than I felt was necessary.  I mean, I try to be succinct, and will often revise something if I feel like the text got away from me, but I'll never apologize for exploring a train of thought to its fullest. 
By the end of the first week I had dropped the course/online school entirely.  It was one of those online colleges that I would later find aren't all that highly regarded; and I didn't find it well organized and didn't want to dig myself into deeper financial hole with them than I already was after a week.