Hogwarts revisited

I have read Harry Potter and the Deathly Hallows twice in the past two months -- the first time, of course, I started the night of it was released and devoured it in about a day.

I then put it aside for awhile, and then picked it back up to read at a leisurely pace. The end made me want to go over Half-Blood Prince again, so I read it.

Today, I decided to start all over again. So I'm halfway through Sorcerer's Stone. As I read, it occurs to me there are a lot of questions still left unanswered. Such as:

• What happens to a wizard's/witch's wand when they die?
• If underage wizards and witches aren't allowed to perform magic outside school, why was Lily Evans never busted for "turning teacups into rats," as Petunia tells Harry upon the revelation of the latter learning he is a wizard? (Page 53.)
• Why was it that Ron couldn't perform simple spells with his broken wand in Chamber of Secrets, but Hagrid, whose wand was broken in two upon his expulsion from Hogwarts, is able to give Dudley a pig's tail and make boats move on their own with the pieces of his wand, stashed in a pink umbrella?
• Furthermore, if the Ministry of Magic does, in fact, monitor magic, why have they never caught Hagrid performing magic?

I'm sure there are more questions forthcoming as I continue to read.