I don't imagine fishing is great right next to an aircraft carrier, what with propellers and sonar and all that fun stuff making noise in the water and scaring fish away?

Fishing from a boat is actually really easy. The hull is quite rich in small crustaceans and flora. This attracts bait fish, which attracts larger fish. A carrier at anchor bunkering would have all sorts of animals swimming around.

Presumably you can turn those off.

As long as there is fuel for the airplanes, couldn't they be used for whaling? How much of a whale is left after being hit by a hellfire missile?

The ASW gear would make for a fantastic fish-finder!