You can't win bounty that you place on other races yourself. You AUTOMATICALLY win any other bounty that any other player placed on any other player when you kill their ships. Bounty is awarded based on the strength of the target. To see if there is bounty that you will win if you destroy that other-party ship, mouse over it and see if it says "Bounty value" in the info panel. Pirates never pay bounty.
2) If you kill all the pirates that attack you in one of their raids, the only "reward" you get is the experience they offer up when destroyed. You need a capship in the area to take advantage of this. If you go to the pirate base and kill them all there and take over the base, if that's the only pirate base on the map (sometimes there's more than one), you won't have to worry about pirates ever again in that game.
-- Retro