Dunno what we really gain from understanding the precise hierarchy and roles. In fact I like the fact that STD uses characters rather than roles on a starship. Gives you a feeling that the people are there for a reason, rather than just filling slots in a roster.
I would prefer a strong mix of both, Voyager and DS9 had well flushed characters as well as a stronger definition of that hierarchy. I think for a show about a ship manned with a hierarchy it just adds an element of aesthetics. Of course, it isn't integral, more of a want than a need. A good solid story with good solid characters is the most important.
I'm going to say: Lorca. (Yes, he has some issues in private but in command he does what needs to b done, and keeps his wits about him.)
Not to me. One look at Michael and his levelheadedness takes a back seat. She bothers him no end and he can't do much about those feelings.
I find that worrying, surely they'd all be level-headed, they are meant to be professionals and officers who have undergone a number of psych evaluations and mental testing before begin allowed to serve in Starfleet (one would assume).