"This planet that I lost also had a starbase. I read somewhere that you can steal PBP from a player when capturing a starbase. So - is that also true when destroying a starbase?"
You got it backwards:
You gain 2 pbp's from defeated player (if he has them) if you destroy a star base. Yes, you get a report in the combat section when you do this. This is also true if the player is dead (FoF'd out while < 1% Military score).
You do not gain 2 pbp's for capturing a star base intact.
Show Media Item - "This planet that I lost also had a starbase. I read...