Will I still have to face the later forms? If I do have to face the later forms, will I lose my boarding party when it escapes?
Killing the crew in first phase means they won't be there in the next two, same if you kill them in second phase: they won't be there in the final, so killing them can be a good tactic as they may trouble you later.
If you kill them all you won't win that phase or overall, instead the ship will go into auto-pilot and will slowly repair all its systems much like the auto-assault scout drones in earlier sectors. It's best to leave one enemy crew alive, maybe the isolated guy on their laser tri-shot; because fighting an AI Boss is much harder than fighting a single panicky engineer.
When the ship flees to its next phase your boarding crew will be killed if they are still on board, same if you destroy it completely with your crew on board, meaning their noble sacrifice won't go down in the credits.