Simple. An aircraft carrier must turn into the wind at high-speed to get sufficient wind over the flight deck to launch & recover aircraft. If you can get say 30 knots across the deck, that's 30 knots extra speed as 'seen' by the aircrafts wings. More lift. Even with steam catapults this is still necessary.
Typically the carriers air wing component flys off to a naval air station prior to the carrier entering port. The only aircraft useable in port would be helicopters.
Yup...I remember launching our helo while tied to the pier at least a couple of times...and that was from a destroyer (an FF actually).
You're right. When the carriers come into port the planes have already left - for reasons you describe and because it lightens the load.
BTW the commander of the Pacific Command right now is Navy. He has been making public statements making nice to the Chinese. The statements were drafted, I assume, at the White House.
Thanks! I understand the Kitty Hawk is still around because the people of Japan still have an issue with atomic powered vessels. I feel they are changing their minds rather quickly!