A: If you play Let’s Keep Doing That (LKDT) and there aren’t any Actions in the discard pile to attach to it immediately, then whatever Action next hits the discard pile is what will be attached. It’s possible that LKDT might sit empty for several turns.
If it happens that several Actions go into the discard simultaneously (as from a Hand Limit, or Discard and Draw, for example) then whoever causes those multiple Actions to be discarded gets to choose which will be attached to Let’s Keep Doing That.