The enchantment Looting can be applied to swords, this will increase the chances of the mob dropping more items than usual and also increases the chances of rare drops. This doesn't affect the experience points that are dropped.
A Looting III enchanted book (via screenshot)
Looting will increase the chances of you receiving rare item drops and it also increases the number of common item drops from killing mobs. The number of common item drops is increased by 1 per level of looting on the weapon for a maximum of 5 with looting level V.
It also increases the chance of rare drops by making a second attempt for the item to drop after the original attempt fails. The success of the second attempt is LEVEL / LEVEL+1. Looting will also increase the chances of equipment and rare drop by 1% per level of Looting.
A sword with looting dropped more leather and meat than a regular ax (via screenshot)
Looting is exclusive to the sword but it can be used with other weapons, specifically projectile-based weapons. To make this work you will need to be holding the sword in your main hand before your target dies, what that means is you can fire a projectile and swap to your sword before it hit the target. You can also do this by launching the projectile from your off-hand. With this method, looting can be used on weapons such as tridents, arrows, etc.
Using a trident with an enchanted sword with Looting (Via screenshot)
Looting will not work in certain situations:
The easiest way to obtain Looting is through the enchantment table, you will require Lapis Lazuli and high enough XP, and a trident to enchant. You can increase the chances of receiving a higher power level of Looting by placing bookshelves around the enchantment table. Other ways include fishing, trading with villagers, looting chests, and using an anvil to apply an enchanted book with Looting on it.
The enchantment table offering Lotting II (via screenshot)
Looting is a great enchantment that will make farming for items easier and less time-consuming. The fact you can use it with projectile-based weapons just adds to its merits. Like most other enchantments it has multiple ways to be obtained but the best one is through the enchantment table.
A. The highest level of Looting is Level III (3).
A. Looting is used for more item drops from mobs, whereas fortune is a great option if players want more items from blocks.
A. No, looting is an exclusive enchantment for swords.