Of course if you intend flying Klingon, you may wish to concern yourself with Fighter Defence. I routinely make myself fly early-mid era D6V, D7V etc. and find they simply don't have the battle-winning appeal they had in Fed and Emp, for example.
Of course. Klingon fighters are appropriately 'industrial' and the CV's ( like the dreaded point defence uber-beast the D6U ) somewhat vulnerable.
The CV/CVL actually work well with a human ally, and can work against an AI solo, but the mission times double - good fun and tactical, but not the best use of your time for the team i.e. Kreug.
As for the regeneration thing, since the fighter groups are so stupid, I think this is fine for play balance - and I have had to fly again and again against Fluf's CVs. Oh, by "again" I mean "again in a new ship and one hour later as I was killed".