Does the magic contained in these run out or something when someone reads them?

What is in a spell book, anyway (since we never get to see the text, at least in Skyrim)? Incantations?

Well, I imagine that scrolls actually combust upon use, burning up into the fireball or ice storm that the user is casting.

The spell books, on the other hand...the same thing happens to them that happens to the flasks and bottles of the potions you drink, I suppose. You either chuck them away like the ignorant adventurer you are, or stick them into the invisible bag of holding outside of your inventory.

Spell tomes didn't disappear in Oblivion, but that wasn't an issue because you didn't buy them. In Skyrim, if it allowed you to sell them back, it'd allow you to get back some of the money you spent after learning the spell. So at least for spell tomes I figure it's just a mechanical thing to avoid a possible exploit.