Do we see any other Federation Ships other than the Kelvin and Enterprise in the film???
Yes. Several. No Daedalus though!![]()
Do the other Federation ships look just like the Kelvin, or are there different designs? I don't want descriptions, just confirmation!
several ships, all less advanced than Ent. different from Kelvin. I think they all had even numbered nacelles, though.

So I take it there really is no discussion or reason for why the Enterprise looks the way it does, more advanced than TOS and all?
Does the Kelvin look less advanced than the Enterprise at least, maybe closer to TOS?
No... I think trying to shoehorn in an explanation would have seemed weird. I think the fact that this is a divergent reality is the most significant explanation for why things have changed.
Kelvin does have several aspects that are akin to original Ent although less advanced. There are touch screens on the Kelvin but lots of nobs too. I think it's a synthesis of 60s aesthetic, Enterprise TV show aesthetic, and what is common knowledge about modern technology.
No Klingons? Then what about those photos we saw of Nero with two of them in masks?
Must be deleted scenes