cajun, not to be rude, but i suggest you take a good look through the help files. you'll find your answers there, and there is other crucial info there that you need to be familiar with when making terrains. here are a couple of quick responses for you anyway:
a port is the 'home base' for a task group (carrier fleet) - if a task group is sunk it respawns at its home port. capture a port, sink the task group, and you get control of the respawned task group. because of this, you have to define which port a task group belongs to.
the supply system (cities, factories) is covered in the help, but basically, having an intact supply system speeds up rebuild times for airfields (and vehicle bases etc) after damage, e.g. fuel, ammo, field radar, etc etc etc. the factories speed up the field rebuilds directly (even more if trains or barges or road convoys are used), and the cities help speed up the rebuilding of factories themselves.