The Key does have to be revealed when found, and remains face up after the swap. If you swapped it for another Key, you’d reveal that one too, then immediately swap it for some other face-down treasure. Repeat until you get a non-Key or run out of face down treasures to swap.
Once it’s face up, it won’t prevent the game from ending because it has no gold value.
The physical ships can be touching, and might have to be because of lack of space, but for gameplay/rules purposes they are only considered to be touching the island at that point.
This would fall under a similar ruling to the one for towing when there isn’t physical space available to place the towed ship, or pinning when a ship’s front mast is removed or repaired. As long as no other ships are blocking the movement, the oared ship is actually capturable (no oarsman, etc.), and the ship attempting to tow it would have enough movement to reach the bow, you can move it in as close as possible and state the you’re towing it. The oars aren’t meant to be a physical barrier of shield of any kind.
That being side, I’m not sure of what scenario could come up where this would actually matter, outside of a player purposely trying to stall the game. If it’s sitting at its own home island, it can be repaired. If it’s at an opposing home island (after a failed raid?) and can still move away using the oar power, it must. Either way, if that’s the only ship the player has left, their opponent(s) can ignore it and just go around gathering up every other last bit of treasure they can get.
If Wolves are on an island and no one has a Musketeer or Marine left in play, any other gold on that island is considered unavailable and will not prevent the “all available gold” endgame condition.
The next player in turn order chooses, unless players agreed on someone else ahead of time. Regardless of who actually picks, the other players are of course free to give “advice”.