I move irresistible faefolk to a battlefield and select an enemy vex in base. Can I react to my move trigger with orange rengar to play it before vex gets to the bf?

Yes. You can play Rengar, Pouncing to that battlefield before Vex arrives.

Here's the sequence:

1. You move Faefolk to an empty battlefield → you become the Attacker (you applied Contested).
2. Faefolk's "When I move…" trigger goes on the Chain targeting Vex in the enemy's base → game enters a Closed State.
3. You (controller of the newest Chain item) have priority and can play Reaction-speed cards. Rengar, Pouncing has [Reaction] and his text says "I can be played to a battlefield you're attacking" — since you're the attacker, he can go there now.
4. Rengar enters the battlefield before Faefolk's trigger resolves.
5. Faefolk's trigger then resolves, moving Vex to the battlefield.

Because Vex wasn't at the battlefield when Rengar was played, her stun trigger ("When an opponent plays a unit while I'm at a battlefield") does not fire for Rengar. You get Rengar ready to fight Vex without being stunned. (FAQ #11573 covers this exact interaction.)