QIf I play an Ancient Elf and return an Archer to my hand as part of the Ancient Elf's Fanfare ability's cost, can I still play the Archer's ability?

AYes. Once an automatic ability has been triggered, it can be played even if the card with the ability has left the field.

QIf I have 2 copies of this follower on my field, and another follower comes onto my field, does each copy's "Whenever another follower is put onto your field, select an enemy follower on the field and deal it 1 damage" ability trigger?

AYes. Both abilities will trigger.