Can melee damage deal critical hits? For example, if you aim for the head, can you do "headshots" with a melee attack?
Yes, Melee damage deals crits; most easily seen on Crystalisks. Note it can be hard to actually see "critical" (and the damage number) pop up when you're in melee range.
The different classes' Melee attacks, while dealing the same damage, "feel" a bit different thus it's easier to get critical his with some than others. I've found it much easier to aim Zero's melee for a critical hit than Maya's, for example. I'm not sure if the actual range/location is different, or if Zero's attack animation just makes it easier to determine the exact point of impact, however.