…For example, if you’re the only one with Keepers, or the only thing on the table is your opponent’s Creeper…can you choose to do nothing?

A: No, you cannot trash nothing. If you play Trash Something and there’s something available to trash, you must trash it, even if it’s your opponent’s Creeper. Likewise, if you play Trash a Keeper, and you’re the only one with Keepers, you must trash one of your own.