Left click on them. Then hit Y. It works for Capital ships too.

I don't know if there is one, within reasonable limits. I certainly haven't hit it in my limited experience. It'd be a minimum of 100k would be my guess.

You can also rename by clicking on the bar just above the picture in the center at the bottom of the screen of the selected unit. As for resources I've played some pretty big games and haven't hit a limit yet. But also remember it seems that fleet upkeep is 75% (at full level) of your income, so even as you grow that 75% eats into your earnings. I actually think that it is wrong to do that way, but it really hasn't affected gameplay. Just takes longer to build up fleets.