Message in a Bottle is meant to just dock the ship at the island, and not potentially act as another Lost, so the ship should be placed at the island in way so that it doesn’t touch terrain if at all possible. Following the standard placement rules for terrain that should be possible the vast majority of the time. In the rare case you can’t place the ship without it touching terrain (perhaps due to house rules allowing terrain to surround an island or something), ignore the terrain while docking the ship, but then apply it normally as soon as the ship tries to move away.
Dead Man’s Chest must be unloaded when you dock at home – that part isn’t optional. You only get to decide how many crew to eliminate, and you can choose zero.
You can trigger it as long as some part of the ship is within S during its move action, even if the ship moves away.
The Mines damage applies at the end of the move, which puts it after any other abilities and effects that happen as part of the move action, including S-boarding and shooting with a Captain.
No. That player will count toward the endgame condition because they can’t give move actions, but assuming there are enough other players still going to prevent that, the player with the fort still gets their turn in the normal sequence. If there’s nothing within range of the fort to attack they won’t have anything to do, but that’s not enough to skip them entirely.
Yes. The same applies to a ship that used Hidden Cove too.
Tentacles (and masts) will not prevent or stop movement if the ship is not pinned.