Question: After Hermione gets out of the Devil's snare she is rubbing her hand - what happened to it?
Answer: When she falls through the devil's snare, there is a considerable drop so she could have landed awkwardly. She also has hold of a vine when she falls through so may have caught her hand that way.
Question: If Harry's relatives hate him, then why are they against him going to Hogwarts to study magic? Why wouldn't they be excited to be rid of him most of the time?
Answer: Because they know of his wizard heritage and they hate it. They think he and his parents were freaks.
Good answer, but I'd add they also knew it was something Harry would very much want, and they would always deny him simply to be as mean-spirited as possible.
Not to mention one of Vernon and Petunia's overriding motivations is to appear normal to their neighbors, and the more magic Harry knows, the less likely they are to achieve that. It could presumably also be dangerous for them, as future books/movies confirm.
1. They were constantly being barraged with letters from Hogwarts in an increasingly disruptive manner. Eventually, this would be noticed as something weird by their neighbors, which is something they REALLY don't want: anyone to know about Petunia's magical relations. 2. They were flat out threatened by Hagrid and terrified on both him and Dumbledore Better to let him go there then have to spend their entire lives on the run without it even working.
They were against it long before the barrage of letters or Hagrid showing up. They knew about the school, Petunia's sister went there and she told Vernon. They don't want to seem weird to the neighbors in general, they aren't afraid people around them will think they have a wizard in their family because nobody believes in wizards.
Question: During flight class, when we see Hermione's broom rolling just above the ground, there is something black in front of the broom. I don't mean Hermione's sleeve. What is it?
Answer: I don't think you mean this but you can see the shoe of the person standing next to her. If you mean on the bottom side of the screen then you can see Hermione (or whoever is standing there) kick the broom to make it move I think. But it's not causing all the movement of the broom though, but there is definite contact with a foot. You can't see the top of the broom (I'd say that's the front BTW).
Answer: It's there to help her wounds from the whole ordeal. You say she would have rubbed her hand for longer but not really. In the heat of the moment she's probably running on adrenaline and just blocks the pain out.
Ssiscool