Regarding carriers, what kind of ship are you flying? If you're in a frigate, I wouldn't expect you to have too much trouble chasing them down. Deploying some faster ships may be worthwhile to help chase them down, in any case.
Depends on the carrier. Condor's base combat speed is only 40 (which is catastrophically slow if it gets into an escape scenario), and Gemini isn't much better at 50.
Heron, however, goes at
90 (I always felt it was fast, but had no idea how fast until I checked the codex). Further, it's a good enough fighter to deal with one or two frigates, or a lone destroyer, that try to catch it; it doesn't actually have much in the way of weapons, but it has a pretty good shield and flux stats to use it with (unlike the aforementioned Condor or Gemini).
The player does pay quite a bit in deployment cost for those benefits, but it remains annoying to run AI Herons down (especially with level 20 officers) if they decide they don't want to stand around and be caught.