Unless the UT specifically says it can be used or applies while still on an island (Altar, etc.), or is revealed when unloaded at home, once it’s on your home island you can’t use it any more.
When you dock at home with a facedown UT that isn’t required to be unloaded as part of its ability, you can choose to keep it on your ship, but must state that it’s a UT. You don’t have to reveal which one it is specifically, though.
Unrevealed treasure that’s removed from the game by sinking or any other means remains unrevealed. The player who lost the ship is free to tell you what was on it, but they’re not required to.