QDoes "If this follower would take more than 3 damage, it takes 3 instead" mean that the selected follower can only take 3 damage a turn?

ANo, it means that any instance of damage dealt to the selected follower will be reduced to 3 if it exceeds 3 damage. For example, if the follower is attacked by two enemy followers with 4 attack, it will only take 3 damage from each attack. However, if the follower is attacked by an enemy follower with 4 attack and an enemy follower with 2 attack, it will take 3 damage and 2 damage from each attack respectively.

QWhen playing this amulet's activated ability, if I choose option 3 and an ability lets me take two consecutive turns, does the selected follower still have "If this follower would take more than 3 damage, it takes 3 instead" during the consecutive turn?

ANo. However, the selected follower will have it for each opponent's next turn.