I have a question about the effect of the card, Genius Alchemist:

E Commit: Choose a card in your card pool. for the rest of this turn that card does not count towards progressive difficulty.

my question is, if the chosen card leaves the card pool, then returns to the card pool, would the effect of Genius Alchemist still apply to the card when it returns to the card pool?

Only if the card remains face-up in play - in other words, it'd only work if the card was added to your staging area faceup and then moved back to your card pool still face-up. If it gets discarded, added to your momentum, returned to your hand, or even moved to the transitional zone to be re-played, it will not keep the effect of Genius Alchemist.

Momentum is in play, so if it goes to momentum face up it's fine.