Actually kill all but one. Leave one alive, I believe the one on the beam weapon is the best one to spare. Dude can't get out to repair any other part of the ship and is on the most useless weapon if your shields are up and can't get out to teleport in as a boarder. Try to kill everyone else though.
The boss ship is formidable but it has that glaring weakness with its weapons being isolated from the rest of the ship that can be exploited.
No, only do this if you're boarding the main ship. If you don't have the proper weapons to get through the shields, killing the crew and using a boarding team to bring down the shields is your only other option. If you do have the proper weapons, a boarding team is both more difficult and more time-consuming. (When doing this, the guy manning the laser weapon is the one you want to leave alive.)
If you're doing the fight the normal way, you want to kill all of the crew members manning the weapons. Standard weapon attacks won't kill the entire crew, and there's no reason to leave the laser operational.