Borderline IMHO. It's true that דב suggests male, because there's דובה for a female bear. But it suggests the maleness weakly, because if you talk about some bear and you don't know or don't care about its sex, then you'll say דב. Now when in English you say "the male bear" then presumably it's important for you to stress that it's the male; and in such contexts, a Hebrew speaker would tend to stress it, too, by saying הדב הזכר.
I think so (as far as I can see form running examples in my mind). At least if you measure "supposed" by how we actually speak and what sound natural to our ears. Not sure what the formal rule is, if there's a formal rule at all at such basic level of the syntax. I think Biblical Hebrew, and probably more recent eras, too, didn't require the copula so categorically, but I don't have examples either way off-hand, except the famous כי האדם עץ השדה.