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 Action cards specifically. Nor will Veto! which cancels Rules stop this type of free action.

More broadly worded Surprises might prevent some of these, however. For example, Skullduggery, It’s A Trap and You Can’t Take This Guy From Me are designed more broadly, so that they can prevent “any game action” which can include the results of Action cards, Free Actions from Rule and Free Actions from Keepers or Creepers. The first two can be acquired in the More Surprises pack.

There might be some confusion on 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, so we would rule that it’s no longer stoppable by the Stop That! Anti-Action Surprise.