Do supply limits apply if you capture ships at a port?
No, you are not allowed to keep them if you are over your supply limit. From page 25:


  Taking Control of Enemy Ports - If the land area connected to a Port is successfully attacked and taken control of by another player, that player may immediately replace any enemy Ship units in the Port with an equal number of his own available Ship units (or as many Ship units as he has available, he desires, or is allowed by supply limits). Excess enemy ships are simply removed from the board.