What is an enchanted book?
According to the Minecraft Wiki, an enchanted book is an item which allows players to add enchantments to weapons, tools, or armor by combining the enchantment book with one of said items on an anvil.
Can they receive any enchantment?
Testing in creative and survival mode shows that books can receive any enchantment that a normal weapon/armor/tool/other can receive. An easy way to check is to go into creative mode and use the new search function to search for the term book. This will show you what all the enchanted books are.
Can they receive more than one enchantment?
According to the wiki, books may only have one enchantment. This can be tested by giving yourself a bunch of books and enchanting them, then throwing them into lava or whatever you wish to do with them.
Since enchantments have different chances of occurring for different tools, materials, and at different levels, how are those probabilities different for books?
This would be different for books since books are not diamond swords. However, this would have that many variables because unlike a sword, books can only be made from paper. Swords can be made from diamonds, iron, and other materials. You would have to test this to truly know, but if John tells us how many levels he invested into his enchanted books, we might be able to know. Right now, though, it appears that the enchantment gives you the highest level (ex. Protection IV, Sharpness IV, etc.)
/xp -5000000L mikeTheLiar
The xp command does not work with negative experience points, but works for negative levels, according to the Minecraft Wiki.
Best Answer
Gnembon covers the problem in his video:
Summarizing his findings, there are three main factors
That last part is the most prohibitive, meaning applying enchantments to a tool one after another will quickly drive the cost way up. The way to approach it is to combine enchantments in form of a binary tree - merge same cost books in pairs (then potentially merge these pairs), treating the original tool as one of the 'leaves' of the binary tree (same as one level 1 book).
When combining books swap their positions in the anvil and always choose the cheaper option, and prefer to merge items of similar cost.