There is another point which wasn't discussed much, but does trouble me : the "outpouring of magic" that happened in chapter 89 when Hermione died.

It's the first time we heard about anything like that happening after a wizard death. It's not canon. It wasn't hinted to before, like Dumbledore didn't speak about it in "pretending to be wise", when he tries to convince Harry souls exist. Harry didn't feel it when his parents were killed. Harry didn't feel it when Rita Skeeter is killed by Quirrell. That's a lot of evidence pointing to it not being the common thing that happens when someone dies.

And yet, Harry doesn't ask any question about it, he doesn't try to know if it happens rarely (and then in which circumstances ?) or frequently, or if it's even an entirely new phenomena, it doesn't ask around if it could be faked, ...

Some possibles explanations :

1. It's the Source of Magic recording the brain state of person when it dies, allowing for resurrection before. But then, why no hint about it before ? Why Harry didn't feel it for Rita ?

2. It's the Source of Magic recording the brain state of person when it dies, but the Source of Magic didn't use to do it. Harry had to hack the Source of Magic to implement it. And he had to cleverly use Time Turners so he could hack it before Hermione's death.

3. Someone made an Horcrux of Hermione, and it's the Horcrux that gives the feeling.

4. It doesn't occur usually, but it does occur because of a bond between Hermione and Harry, be it just "love magic" or be it with Hermione being bound to House Potter.

5. This is purely faked (either memory-charm, or a fake feeling) by either Dumbledore or Quirrell (maybe using a Time Turner) to try to convince Harry that Hermione is really dead so he doesn't do any folly to try to save her (but then, it seemed to fail).