Succession After Henry I: Matilda or Stephen

I'm far from an expert on the period, but will throw in my tuppence worth.

1. The simple answer would be Matilda. She was Henry I's only living legitimate child, he had named her his heir and the barons had acknowledged her as such. However, Henry hardly had all that great of a claim to be king himself. He probably had one elder brother murdered to get England and certainly deposed another elder brother to get Normandy. And his barons most likely were under duress when they acknowledged Matilda as the heir. What's more if female succession is to be allowed in Matilda's case, perhaps Stephen had a claim in that he was the son of Henry's (possibly elder) sister. Although we tend to think of succession as going to the eldest living son then defaulting to the eldest daughter, such rules were not set out at the time (I believe they weren't finalised as such til Henry VIII's time). It could therefore be argued that a male via a female line might have been considered more legitimate than a female via the male line. Finally, Stephen was well known and liked by the English court, who barely knew and strongly disliked Matilda who was apparently very arrogant. With the dynasty of William I already pretty shaky, having the support of the barons should count a lot.
So, I would still say Matilda but Stephen certainly had a strong claim too.

2. Absolutely. Had Robert not been captured after Stephen then she had a huge chance. She also could have done better had she lured more of the barons over to her cause or not offended those who were on her side.

3. I'd call it a draw. Stephen got to be king of England, Matilda had to settle for the duchy of Normandy. However Stephen had to disinherit his sons in favour of Matilda's son who got England and Normandy (and Aquitaine besides). So I'd say Henry II won, while Matilda and Stephen broke even.

4. She lost a powerful ally with Henry Bishop of Winchester, then besieged him and lost Robert in the process. She also turned her allies and the people of London against her. Really, she had the country there and lost it due to a complete lack of personal skills and political nous.

5. Possibly. Empress Matilda seemed prone to cock-ups so she may have messed up even without the other Matilda's interference. But certainly Matilda of Boulogne played a critical part in the whole thing.