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.)
Best Answer
In the current version of Minecraft, there is no way to do this without using mods or creative mode.
If you would like a workaround to split books and have cheats turned on, you can split it using creative. Type
/gamemode 1to switch to creative, then take each of the enchants on your book as separate items and destroy the original. Switch back to survival with/gamemode 0and act like nothing ever happened...Note that this approach will not work if you aren't OP on a server or have singleplayer commands off.