In my case...
Yes, I pilot my ship. Since it is one of the bigger ones, it has no chance to catch smaller ships, unless it is a carrier. I tend to use Legion frequently late in the game because it is capable of forcing fights against a wide variety of targets and be a match against an enemy battleship. Even in midgame, when I had a choice of buying either Eagle or Heron, I picked Heron because I had trouble forcing fights with Medusa. In difficult fights, I pilot quad lance Paragon. Slowest there is, but devastating to anything short of a battlestation if they wander into Paragon's shot range.
I use Steady officers (because my fleet commander is Steady by default if given to AI control). In the few 0.8 games I played, I do not bother leveling them up because 1) I was too lazy to save scum their skills. 2) For my first game, I wanted to see how far an unskilled character could go.
Eliminate is risky. It often plays into the cowardly enemy AI. They simply retreat more and your ships get encircled and overwhelmed. Once the battle is mostly decided, it is safer to Eliminate and mop up. Of course, sometimes, even Eliminate is not always aggressive enough.
Reckless AI, assuming that is what Remnants use, is not immune to cowardice. I have seen Remnant frigates fight like Spathi too much. Feels like I am playing Spathi vs. X in Star Control more than Starsector.