Healing Ships?

I assume you can heal ships by getting them back to port.

Some questions....

• Do you just need to be adjacent (within radius) of port?
  • (I dont seem to be able to move onto or select a city or port)
• Does the port need to be of a certain size?
  • Can only lvl 3 ports repair or something?
  • Do battleships need a bigger port to repair than a submarine

thanks in advance.