I think re-basing is buggy. You can re-base to any city on the map (marked green or not) and the plane re-bases to it or I have misunderstood something.
Regarding what the AI do whit their planes or not, I have found out that they don't usually use biplanes or fighters offensively. I have seen damaged deployed fighters, but I don't know what they have done. They use bombers sometimes and they also use jetfighters offensively. Although not nearly as much as they could have done. They still idle with their planes a lot. My neighbour civ was nuked, twice by two jetbombers. That was scary. Making me wonder. Ar. e fighters able to intercept bombers. I have seen dogfights but that was fighter vs. fighter. I have yet not seen a fighter vs. a bomber so I don't know how effective that would have been. Probably like Civ 5, you need to kill the bomber in order to stop the nuking and that is unlikely.