But who am I to knock out your theory? You're right, it doesn't seem like Dumbledore is though with us yet, and the phoenix has been brought up on so many occasions. Why would Jo spend so much time telling us about the phoenix is it wasn't important?
The bottom line is, I have no idea, lol. This is all just speculation.
I think Half blood Prince means both. It plays up his magical side, and it also means that he's proud of his mother, which was where his magic came from in the first place. So he's proud that half of his blood, I guess, is magic, and he's proud of his mother's side, where his magic came from.
I didn't understand why she called the book Harry Potter and the HBP. I get that the HBP helped him out (as much as Harry hates him now that he knows the prince in Snape) but it didn't seem to have a lot to do with the plot. I think 'Harry Potter and the Six Split Souls', or 'Harry Potter and the Horcruxes of Voldemort' or something (I know those are terrible, but you get my drift, right? Something about Voldy splitting his soul) would have been better, since they have more to do with the plot. But maybe the half blood prince pops up again in the 6th, who knows?
I don't think there was too much significance in the first chapter, except that the evils being preformed by Lord Voldemort and his followers are now affecting muggles as well. I could be wrong though.

Some people are saying Amelia Bones (don't ask me where the 'R' went, I'm not the one who came up with that theory

Oh, and J.K said that Malfoy is "not a nice man", so I guess that means he still isn't a good person, even though he didn't kill Dumbledore.