The final chapter
It is well reported that J.K. Rowling has said that she wrote the last chapter of HP7 a few years back, and that the last word of that chapter is "scar." Thinking about this, it tells me that it is very likely that the last sentence talks about Harry and has his famous scar as the object of the sentence -- since in English sentences only end with a noun if that noun is either the direct or indirect object of the sentence or the object of a prepositional phrase. Many of the sentences I can think of that would end with "scar" would refer to a living person. Since the reports also contend that this chapter is an epilogue of sorts that covers what happens to the characters after the end of the main story, I think that we have reasonable, but far from certain, evidence that Harry will survive.
Unexpected magic use
Another rumor I've heard, which is similarly reported as coming from J.K. Rowling herself, is that in book 7 someone unexpected will use magic. Now it is possible that this could be a new character, but I highly doubt it. This is the final act of the story, so most of the significant characters should already have appeared on stage. So, this leads to the question of who we've seen that will use magic that we would not expect.
It is very easy to rule out the wizards, house elves and other known magic creatures since we've seen them use magic regularly. This leaves us with the two squibs -- Filtch and Figg -- and the muggles -- the three Dursley's. Since the use of magic by a believed squib would not, at least in my opinion, qualify as "unexpected" that leaves us with the Dursley's.
Before last week's readings, I would have suspected that Petunia was the likely candidate, since she has been shown to know more about what is going on then was previously believed. For a while I even wondered if she wasn't a squib herself. However, I've seen reports attributed to Rowling confirming that she is a muggle, which reduces here likelihood of being the unexpected user of magic.
However, it is clear that she could potentially carry the gene for magic. Which means her child, Dudley, could also have a potential for magic, albeit one that hasn't manifested before. Since we don't know if dementors have a taste for non-magical souls or not, it is possible that the one that attacked Dudley in the opening chapter of book 5 sensed a latent talent and that is why they didn't ignore Dudley.
The Black Family Tree
Canonical portions of the Black Family tree are readily available on the web (on the Harry Potter Lexicon, and on wikipedia at least). From these, we can see that in addition to the known Blacks -- Sirius, Tonks, Bellatrix Lastrange and Narcissa Malfoy -- and the other suspected relations -- both Arthur and Molly Weasly and, but extension, their children -- that there are both Longbottoms and Potters on the tree. I suspect that in book 7 it will be directly revealed that both Harry and Nevile are also related to the Blacks, and are distant cousins to both their friends and enemies at Hogwarts.
While I don't have any ideas about some of the bigger issues, like who will survive the final book, I do have some other ideas of what will, or at least should happen.
- Harry will reconcile with Draco, and may even be able to bring Draco around to his side
- Harry may reconcile with the Dursley's
- Harry should reconcile with Snape, but it will be harder for him that facing Voldermort
- Despite his claims to the contrary at the end of book 6, Harry will end up returning to Hogwarts in some capacity, possibly even as a student
- The Wizarding World will be turned on its side in a bigger way then expected
If I come up with something more, I'll reserve the right to re-edit this, or comment on my own posting.