Can you re-roll the die roll for the Duel event, if the chosen crew are on the same ship as a re-roll?
No, for the same reason you can’t reroll a Marine. The roll is being made for the crew, not the ship they’re on.
Can a home island raider dock at an enemy home island if there aren’t any coins there?
Yes. You just won’t get to steal anything.
Pretty sure I’ve asked this but not seeing it via the forum search: If you start your turn on a sargasso sea but you didn’t get stuck last turn, do you have to roll since you’re sailing over it? Or would you only roll if you contact a NEW sargasso sea during that action?
You don’t get stuck (or have to roll) immediately if you start on it, but when you move if any part of the ship is still touching the terrain after any segment, you will have to roll again.