It is best to not get hung up on things too quick. Concentrate on unlocking all chapters first, yes.
You don't have to leave the ship, but you can any time (after he first called you). The game lets you "rewind" after the credits and you'll be back on board. There is even a hint hidden in the ending, but you don't necessarily need it.
Almost done. There's a few characters left whose fate I assume I can only figure out with the Bargain chapter, plus one extra triple. There's only two possible solutions, but I want to deduce it instead of guessing. I'm totally out of ideas, though.