A: Of course ideally you’d trash someone else’s. Only if you have the only Keeper/s on the table would you be forced to trash your own. The same is true if you’re forced to play Trash A Keeper and yours is the only Keeper on the table — you have to trash one, and if yours is the only one available, you have to trash it. But if someone else’s is available, feel free to trash theirs!
See also: If you play Trash Something (or Trash a Keeper), can you choose not to trash something?