I am well aware that face down attacks made from effects such as Chop and Alex don't go to momentum, and that Multiple copies of attacks do not go into momentum at any time, but if I were to use The Masters' Challenge or Warrior Poet and then use Felicia's F to put my card pool into my momentum, would those cards be discarded or go into the momentum?

if they arent multiples then yes they go to the momentum. the rules only say what happens to them at the end phase.

Stamp for Ziepnir. Facedown cards CAN go to momentum - there's nothing that says they absolutely may not - except for multiple copies, which DO have an effect on them that says they may not be added to momentum.