Some cards say things like “If you discard one of your Keepers, you can move this Creeper to another player,” or “You can discard an opponents Keeper, but you have to move your own Keeper to them,” or “If you discard X cards from your hand, you can draw some more cards and play them immediately.” Do those moves or discards need to be caused by an Action or Rule, or are they part of the card’s stated function?

A: You do not need some other means of moving or discarding the cards in question in order to utilize the function stated. The movement or discard is part of the function itself. Usually there is some benefit, and the move or discard is part of the “cost” or “sacrifice.” It would be far too limited if these moves or discards had to occur organically through some other mechanism in the game.

See also: If a Creeper says I can get rid of it if I “discard a Keeper.” Does this mean voluntary discard…
And also: If I have a Keeper which says I get some benefit from discarding or moving it…