A: Those are not considered “Actions” in the sense that they are not Action cards, and Stop That (or Belay That) is intended to cancel out the playing of Action cards specifically. Nor will Veto! which cancels the playing of Rules stop these types of Free Actions. The Surprise you’re looking for is one found only in the More Surprises pack, and it’s called No Free Lunch.

There are a couple of other more broadly worded Surprises that prevent some types of Free Actions, however. For example, Skullduggery, It’s A Trap and You Can’t Take This Guy From Me are written so that they prevent “any game action” which causes Keepers to change hands. This can include the results of Action cards, Free Actions from Rule and Free Actions from Keepers or Creepers. It’s a Trap is in Batman Fluxx and Star Fluxx, You Can’t Take This Guy From Me is in Firefly, and Skullduggery is a promo card which can be found in the More Surprises pack linked above.

There might be some confusion on using the Action attached to Let’s Keep Doing That, since there is an Action card permanently in play, but it is intended to act as if it were a New Rule that grants a Free Action, so in functions like any other Free Action, and is covered by the first paragraph.