1) I think Nick pretty much expressed it perfectly... if you want to remain a spirit.. like if you don't have any regrets, if you want to tag along.. it's kind of like the wussy way out, if you refuse to go to the next step. I believe it's something in your soul that does this. Sirius, having seen Harry Potter, having fought bravely, and realizing that HP isn't James, wants to be with him, I believe. He also knows he can't help any more, ever, as a spirit, and so his soul was prepared to leave.
2) I believe it's more because of how Snape actually taught DADA, that one day he substituted. Dumbledore knows how harsh of a teacher he is, and doesn't believe he is suited for that specific position. Also, it may be hard to get a potions teacher as good as he is.. he's apparently immaculate at making potions.
3) He won't. Hence the bodyguards everywhere, all the time. If he goes to Hogsmeade, I'm sure Tonks will be there disguised, or something like that.
4) Well, with Dumbledore's houler to Petunia, I think things will slowly change... each book Harry has more and more power of what he can and can't do in the house... and now that they know that the Aunt has some knowledge.. it seems like things might shape up a bit for them. Also in one of JKR's interviews, she mentions that things "start" to go bad for them in book 4... as if they'll continually get worse for the dursleys.
5) Well, I think Harry's pretty much come to terms with that before the prophecy was said, people have been trying to kill him for 5 years, so knowing that someone has to kill him to survive wouldn't be all that much of a shock. However, knowing that *HE* has to kill Voldemort is probably much more upsetting, as he's never killed anyone before.
6) I think the guilt was when he tried, and tossed it and the glass shattered, although I wouldn't be suprised if he puts a picture of sirius in the frame and repairs the glass. I think that there will be a long period of time where he'll try to imagine what advice Sirius will give him through different periods... and I'm pretty sure the line "For Sirius!" will come up in the final fight between Harry and Voldemort. Hopefully it'll be done well, and not with too much cheese.
7) No, I don't think so.. but Harry will at least be more tolerant of Snape. Then again, Snape simply ignoring him is a lot better than it was before. Harry's at the age, though, where I don't see him apologizing to Snape for his parents behavior, or his.
8) I don't think they will, I think that members from each house will get together, but I don't see the whole school rallying together. I don't think that all of Slytherin are EVIL, just... power hungry and selfish. Malfoy, Crabbe and Goyle though.. I don't think they'll ever see the bright side of the coin.
9) if Umbridge is caught I'm sure she'll be sent to prison, but remember the Dementors have fled Azkaban, so that prison's pretty useless now. And now that the Ministry has admitted to Voldemort's return, the corruption will die down quite a bit, I think.
10) Well, you have to accept that your parents were right old ba$tards sometimes.
I think it'll help him feel better about who he is, knowing that when his dad was his age, he was a prick. It does change things a bit... but he's at the age when you realize your parents don't know everything.. so it's pretty well timed. If he thought his parents were perfect until he was 17 or 18, then it might have caused some more trouble for him.