As far as I know: No you can not make more than one ship per turn per planet. It's not needed, really. The ships are supposed to be more Star Trek-like, as in you have less but each is more important. Besides the cosmetics it's not that different in terms of gameplay, though it may be easier to manage.
There is no tactical level combat. The developers went the Civ route again, citing how tactical battles tend to take over games because they take too much time out of the larger game, and that tactical combat AI (your own and the enemy's) tends to bite.