A: You could certainly put either of these New Rules (Get On With It, or Swap Plays For Draws) into play as part of an Action like Draw 3 Play 2 of them (D3P2) or Draw 2 and Use Em (D2UE), or Fizzbin (or your cards drawn via the Rule Goal Bonanza) but you could not utilize their functions while in the middle of executing one of these cards. While all four of these Actions/Free Actions do give you a sort of temporary hand, you can’t substitute it for your real hand to “discard and draw back up to 3”, for example.
You would either need to invoke Get On With It! before the Free/Action with the temporary hand is played or after. The Playing of D3P2/D2UE/Fizzbin/Goal Bonanza, and all actions as a result of it are considered 1 “Play”.