A native speaker wrote me in an e-mail the sentence "He's quite the diva", referring to another guy. What does this exactly mean? Is it formal, informal, slangy?
Could you say also "He's quite A diva"? It would maybe sound more reasonable grammatically....
'Quite a' is more normal grammatically, and would fit with any degree of formality. 'Quite the' is idiomatic and informal, the sort of thing I might expect to hear in a situation comedy. It's hard to say what extra it conveys: a bit of either sarcasm or admiration, perhaps. I think only used of people: it's quite a problem, but not quite the problem. It suggests some kind of archetype or high degree - not the lukewarm BrE 'quite' if 'quite a hard worker' meant "works fairly/reasonably hard". I might expect to hear someone described as quite the expert / blue-eyed boy / hero of the day.
'Diva' is informal for anyone who isn't actually Maria Callas or the like, of course. Any man, for a start.