There are 3 playthroughs in Borderlands 2: Normal Mode, True Vault Hunter Mode and Ultimate Vault Hunter Mode.
During the first playthrough, all quests are just set at a certain level, and the rewards stay the same throughout the entire playthrough. This playthrough ranges from level 1-30ish
The second playthrough, starting at around level 30, works in almost the same way, except once you beat the playthrough, everything scales up to level 50 (by this I mean most enemies will be 48-52). Every quest, reward, enemy, everything scales up.
During the final playthrough, all enemies will be scaled above the highest player's level, and while I'm not 100% certain, I believe the quests function the same.
So during the first playthrough, complete the quests whenever you want as the reward won't ever be better than when you can first complete it; however, during the second playthrough, I try to leave as many quests as possible (I'm fairly familiar with the quests that give good items, so certainly I leave those) until I've beaten the entire mode, then everything will scale to level 50.
During the first two playthroughs, quests can only be completed once per character; however, in your final playthrough you can reset your quest progress. When resetting, you essentially begin back at the beginning of the playthrough, so you can't selectively reset quests.
With the exception of bosses dropping some items (not loot) for quests, bosses can be farmed over and over and can drop the same thing. Often there are tiny variations on loot, so even though you may get the item you want, it may not have the stats that you want, so you need to keep farming.