QDoes summoning a Fairy with this amulet's Fanfare ability count as playing a card?

ANo, it doesn't.

QCan this amulet's Strike ability deal damage to an enemy follower with Aura?

AYes, it can.

QWhat happens if a follower with the Follower Strike ability from this amulet attacks an enemy follower with 2 defense?

AThe attacking follower remains on the field in an engaged state, while the enemy follower is destroyed.

First, you select the enemy follower as the attack target and engage the attacking follower. Then, during the following Confirmation Timing, you resolve the attacker's Follower Strike ability, dealing 2 damage to the enemy follower and reducing its defense to 0. The enemy follower is then destroyed. As there is no longer an attack target, the attack ends without the followers entering combat, and the attacking follower simply remains in an engaged state.