Minecraft – Can’t enchant diamond sword

As far as I could tell from experimenting, the enchantments provide random effects, but the level of the effects is based on experience spent. So, an exp-level-5 enchantment is much more likely to be a level II or III version rather than a level I version. A sword with "Sharpness V" does a lot more damage than one with "Sharpness I", for example. It'll be a much higher-level enchantment spell, too.

Some enchantment spells create multiple effects, and I think the total level of all effects is equal to the spell level. So, a Level-I sharpness plus a Level-II Fire Aspect would be something like 7 exp levels (2 for sharpness, plus 5 for fire aspect). I need to figure out the actual exp level to enchantment level curve, but I think each level (I, II, II, IV, V) requires substantially more experience.

Yes. The height limit is two.

Only bookshelves the same height or one block higher than the enchantment table are counted when setting the maximum level the table can enchant. Additionally, only bookshelves exactly two blocks away from the table are counted, not bookshelves directly adjacent, nor bookshelves further away.

There is a popular version which was necessary until the changes in version 1.3: A two-high 5x5 square of bookshelves with a single one block wide door way, separated from the table in the center by a 3x3 square path of absolutely nothing except air. It's important to note anything placed between a bookshelf and the enchanting table will prevent the bookshelf from contributing to the table's maximum level.

There is an upper limit on the enchantment table's level. Beyond 15 bookshelves there is no additional effect to adding more, so there is no need to build this entire structure since version 1.3. With just 15 bookshelves in any of the valid positions you can achieve the maximum enchanting level which is 30.