You should keep posting these at MT until the site actually dies.
Is Runes of Death eliminated immediately after the elimination of the final mast or crew on the ship, or must you wait for the effect to trigger at the beginning of your next turn in order to get rid of it?
It’s eliminated immediately if there are no masts AND no crew on the ship. This can happen when the last is removed, or if it transfers to a ship with none.
With Message in a Bottle, does the owner of the ship choose where the ship is docked AT the island once your opponent chooses which (tied) island the ship docks at?
No, the opponent chooses only the island when there’s a tie. You still have control over where specifically the ship becomes docked at that island.