Should I throw away books with black mold in them?

Yes, sorry, yes. I know it's painful, and you'll feel like you're burning the library at Alexandria, but yes. They must go. They will infect your other books.

Check to make sure they aren't one-of-a-kind. If they are, you might want to contact a university or local library about scanning them before tossing them. Or maybe they'll have some hints about how to restore them.

But if they are paperbacks where you can easily buy them from amazon for .01, then you must put them out of their misery. They've done their best, it's time to go.

Yes.

Yes, breathing in mould spores is bad for you. If they weren't mouldy when you got them and you were storing them in the house get someone in to have a look at it. You may have a damp problem.

yes