A: The first answer is very easy: No. D3P2 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 use with Let’s Keep Doing That.
Technically, you should execute the instructions on D3P2 in the order stated: Play 2 of them, and [then] discard the last card.
So you play D3P2. It’s not technically in the discard pile yet. Then you play, from your mini-hand of 3 cards, Let’s Keep Doing That. Nothing in your mini-hand is in the discard pile yet. You must pick your Action out of the discard pile right then, as part of your play of Let’s Keep Doing that, so, no, the last card from the D3P2 is not yet in the discard pile, available for use with Let’s Keep Doing that. It will be after you’re done playing both of the cards you choose to play, and not before.
Note that this ruling will also apply to Draw 2 and Use ‘Em (D2UE) and Fizzbin. Cards executed from your temporary hand are not in the discard pile until the whole Action is completed.