Voldemort: He's the key, I think. Why did he want to kill Harry? I think we want to be careful here. First of all I think we're going to learn the answer to this one in OotP. Second, this could be so cliched, so wrong... We cannot have a "Harry is V.'s grandson" thing, or a "Harry is the Chosen One" thing unless someone has a really, really good rationalization.
What I would suggest is something understated and pretty certainly wrong. What if it's just that James and Lily pissed Voldy off and he went after them? He's not the sort to do things halfway. But for whatever reason he spares Harry. Compassion? Amusement? The idea of raising Harry to be the opposite of his parents? I'd say the second is most likely.
Harry: What does he know of his parents' death? I think we could go with the theory that Harry thinks his parents worked for V and were killed by rebels. V then adopted him out of a sense of loyalty to James. That way when he finds out the truth it's much more powerful.
Why does he change? Please, not because he falls in love with Hermione - or Draco, for that matter - and it Changes Him Forever. Most reasonable to me is that he slowly discovers everything he thinks he knows is a lie. Also, book-Harry has this deep admiration for his father. I think we could play this up even more in Alternity, so when he learns what his father really believed, it could explain a lot.
Dumbledore: he's dead. That's it. Unless someone has a really good reason why he wouldn't be. I cannot picture Dumbledore running and hiding, even for strategic reasons.
Snape: Well, the logical thing is that he's dead too, but that takes away a character we can have so much fun with! I say he's alive, and either in really deep cover, working for V and hating it, or in with the resistance, but eyed with tons of suspicion. Either way has fair opportunity for loads of angst. Can you imagine Snape with even more self-loathing?
So, pick away. Let's hear some other ideas!