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 select 2 enemy followers with this follower's ability, does it deal 1 damage to each of them?

AYes, it does.

QIf I have 2 copies of this follower on my field, and another follower is placed on the field, does each copy's ability trigger?

AYes. Both abilities will trigger.