A: The first answer is very easy: No. Draw 3, Play 2 of Them (D3P2) (or Draw 2 and Use ‘Em: D2UE, or Fizzbin) does not technically go in the discard pile until you are completely done executing everything on the card.

You also seem to be asking whether the card you don’t play from D3P2 is in the discard pile, available to pull out and with one of the other cards.

Technically, you should execute the instructions on D3P2 in the order stated: Play 2 of them, and [then] discard the last card. D2UE and Fizzbin don’t involve any discarded cards, so that point is moot where they’re concerned.

All other cards that you play in the process of executing these cards, however, go into the discard pile in the order they are used, and are available to be pulled and used by subsequent cards.

Cards which allow you to pull an Action from the discard pile are:
New Rule: Let’s Keep Doing That
Action: Let’s Do That Again
Action: Time Portal (which ends your turn immediately as soon as you use it)