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.)
Run a execute command on all players that are holding the tool which sets the tag on all items you want the tag on:
Run these once:
/scoreboard objectives add holdingTool dummy
/scoreboard objectives add tagItem dummy
/scoreboard objectives add life stat.timeSinceDeath
Run these on a clock:
/scoreboard players set @a holdingTool 0
/scoreboard players set @a holdingTool 1 {SelectedItem:<Tool>}
/scoreboard players set @e[type=Item] tagItem 0
/scoreboard players set @e[type=Item,score_life=1] tagItem 1 {Item:<Data Tags of Item>}
/execute @a[score_holdingTool_min = 1] ~ ~ ~ entitydata @e[score_tagItem_min = 1,r=5] {Item:{tag:{CanPlaceOn:["<Block That Can Be Placed On>"]}}}
This will run the entitydata command on all items around players in a 5 block range with the holdingTool tag of 1, aka all players who have the specific tool selected. the entitydata command will only affect items of the correct type that has just spawned.
Best Answer
As correctly noted by Thorsal, the durability of an 'Unbreaking' item is not fixed, but depends on chance.
More specifically, the number of uses you will get out of a given tool will follow a binomial distribution. This is the same statistical law that predicts things like "how many heads will I get out of 100 coin tosses?"
Consider that a diamond pickaxe normally has durability of 1,536 uses. If you plot the binomial probability density function (PDF) for 1,536 'successes' with a 'success rate' of P = 1/2 = 0.5 (Unbreaking 1), P = 1/3 = 0.333 (Unbreaking II), and P = 1/4 = 0.25 (Unbreaking III) you get the following graph:
This shows that an Unbreaking III Diamond Pick will last, on average, about 6,144 uses (four times as long as a normal Diamond Pick.) However there is also a chance it will break after only 6,000 uses. Similarly, there is a chance it will last for 6,500 uses.
However there is basically no chance it will last longer than 7,000 uses, or less than 5,000 uses.