1) There are some cheaty ways like using x-ray glitches or a terrain mapping program like Minutor, but generally, you just have to explore.
2) You can add enchanments to a tool via an enchanted book or using another enchanted item of the same type to merge enchanments. Both of these require crafting an anvil and cost XP, they can be quite expensive depending on the enchantments, enchantment levels and whether the item has already received enchantments this way (there are limits). Enchanting an unenchanted item on the enchanting table can give mutilple enchantments ... you will also need to know which enchantments are compatible with any given tool and/or each other. Suiggest you look at the Minecraft wiki.
3) The enchanments on the table stay to whatever they currently are til you perform any level enchantment on anything compatible with the table, and it will change all of them. For instance, placing a sword on the table might say you'll get Sharpness III, whilst an axe might say Efficiency IV. I place a book on and it says Silk Touch, so i enchant the book. The next book i will try will now have a diff enchantment offered (and by that token it could be the same) and if you put the sword or the axe on the table they would have diff enchantments too.
I forgot to also add in regards to 3) that the three Enchantments the table shows depends on the number of bookcases - for instance if you had the max 15 bookcases the level 3 enchantment would be 30 (the highest), and the other two less. If you changed the number of bookcases i.e in the example removing one so you had 14, you'd get three diff enchating levels, and the level 3 enchantment would be something like 26, 27 or 28 and these can be diff enchantments to the 30 one, and so will the other two. Thats why some people, like myself, have an adjustable Enchating table, which can be anything from manually removing bookcases temporarily (some people temporarily "block" them by placing a torch on them on the face facing the table - the torch is enough to diasble the bookcase) to having an automated redstone one (as i have). Although the lower the number usually means lower level enchantments (example Looting I or II as opposed to Looting III) you can still get some good stuff. I was reminded of this a few mins ago when i finished a play session and had 31 XP, so i looked at the table to enchant a book but the level 30 enchantment was rubbish, so I used the adjustment method and low and behold, when I only had 9/15 active bookcases, the level 3 enchantment (Level 16) was Silk Touch which i snapped up thank you very much!
Somewhere in the Wiki, there is a graph showing probability ao all enchantments versus the level tried. Can't remember exactly where it is cause I coppied it to a ned document I keep in my files to reference. Helps a bit in selecting number of bookcases to activate.