"Riddle Me This!"

brimfin, I'm with @volver and tarathian123 that, unless we're counting minutes at birth (what I presumed), the only answer can be 9+2+2 (what Tarathian presumed).

Oh, Volver got it right! But then what about the piece when you said ?

It's an old question, why the dying message would occur. Indeed, it's one of the great problems of the detective story: why would anyone go to these lengths at all? Why would a murderer kill his victim in a locked room rather than simply bop him over the head in an alley outside? The simplest answer may simply be because it would be damned dull to read about that. You either accept the preconditions of a genre, or you don't. 

Suffice it to say that dying clues have occurred in real life and been absolutely incomprehensible. In Ellery Queen's (Barnaby Ross's) The Tragedy of X, Drury Lane devotes a whole monologue to the question of why someone would tell a message before dying, rather than the murderer's name (if he knows it). The human mind, especially before death, goes to some strange thoughts and conceptions.

As for my story, however, there's a very good reason why Johnson wouldn't say the murderer's name. He was working on the puzzle before death, and he's going in and out on consciousness, as Sgt. Mack tells us. He's not exactly reasoning in that moment, but his mind is going to what he was doing when the murder occurred. I don't think that's all that implausible. If you are dying, you don't know what you will be able to say, but you want to get out some sign, some clue. By drawing attention to the pattern, he can be sure that someone will find the murderer who does not fit that pattern. 

P.S. One can similarly find fault with any riddle. Why would Joel not just say his children's ages? That's highly implausible and makes him seem like a jerk. But you have to accept preconditions. "Willing suspension of disbelief," you know?

How can one possibly determine who has the fish if we don't know what the animals (except the dogs and cats) are? Therefore, I'm tempted to say it's the Swede, because of Swedish fish. 

EDIT: If, on the other hand, Einstein did indeed develop this puzzle, my joke cannot be the true solution, as Swedish fish were developed in the late '50s, and he only lived to '55. 

EDIT AGAIN: I read it once more, and, yes, I am a fool; horses and birds are also in the puzzle. With that said, there's no stipulation that one of them does own the fish, is there?

The preconditions only state that each homeowner owns a certain pet, not that one of those pets is a fish. (The question asks, "Who owns the fish?" but the answer could be "Bob" or "no one.") While this lack of a definitive statement on the matter would not be a problem with most things, this sort of thing can easily be confused for a riddle--it's similar to a riddle I've heard before--in which the point is that no one owns the fish, and you're supposed to overthink it with mathematical analysis (not my strong point, at all!). I've now looked the puzzle--but not the answer--up online and seen (1) that it does indeed call for detailed logical analysis (something I really cannot do--I don't have a mathematical mind) and (2) that others have criticized it for not having this prerequisite. I feel a bit like Chesterton's sailor now.

It's not that calling it a fish "annoys" me, merely that the fact that a fish is never mentioned in the... Let me put it a different way. Let's forget about the fish, as you say. At the risk of seeming mathematical myself, I'll express it with Animal X. We are told that five animals belong to five houses, right? But we are never told that one of the five houses owns Animal X. The first time that Animal X is mentioned is in the question, "Who owns Animal X?" The answer can be anything. We have to make an assumption, unwarranted by the text, that one of the owners of the five houses is indeed the owner of Animal X. As one source puts it:
While, in most cases, that assumption would not be all that illogical, it's something to watch out for with riddles and puzzles. Preconceptions and assumptions trip us up. 

I'm only going on about this--mea culpa--because I thought it was a riddle, where there's some trick to it, rather than an exercise in pure deductive logic. While I can do this type of thing on a small scale (e.g., your murder puzzle), I tend not to be able to do it on a large scale. Or, at least, so my math teachers used to tell me.