(Long-time lurker; first post)

Some points from earlier chapters that remain unclear to me: any insights would be appreciated?

1) Why did Neville's remembrall go off so vividly in Harry's hands? Also, how are there now two remembralls?

2) Do we have any more information/guesses about Trelawney's prophecy that Dumbledore cut off? What starts with 'S'?

3) Who told Harry to look for Hermione on the train? The writing is ambiguous, and it's not really clear why McGonagall would've wanted them to meet. I guess other theories are worse, though.

4) What's up with Harry's father's rock? Just a way for Dumbledore to encourage Harry to practice transfiguration?

5) Why are we so sure Dumbledore burned a chicken (or transfigured something)? His explanation makes total sense, and Harry's confusion at the time is well-explained by his lack of familiarity with phoenixes. It seems more reasonable to assume almost-burned-out phoenixes look like chickens than...whatever the alternative is.

6) Who is saying "I'm not serious" in Azkaban?

7) Is the "terrible secret" of Lily's potion book really that Snape and Lily fought about it? That just seems like a bizarre reason for a friendship to end. Were Dumbledore's suggestions incorporated into the potion Petunia took?

8) Why did Quirrell leave a polyjuice potion in Bellatrix's cell? (especially since the crime was meant to go unnoticed)