QIf I have two copies of this follower on the field, does each copy's automatic ability trigger whenever an amulet is put onto my field?

AYes, they do.

QIf I evolve an Eidolon of Madness on my field, does this follower's automatic ability trigger?

ANo, it doesn't.

QCan this follower's automatic ability trigger during an opponent's turn?

AYes, it can.