QIf this follower fights an enemy follower with 0 attack, does its automatic ability trigger?

ANo. A follower with 0 or less attack doesn't deal damage during combat.

QI have at least 10 cards in my cemetery, and an opponent targets this follower with Usurping Spineblade, dealing 3 damage and then 2 more damage to it. If it started with 5 defense, can I search my deck for a Serpent Drake and summon it?

ANo. While this follower's automatic ability would trigger 2 times, it would no longer be on your field by the time you resolve the ability, as it was destroyed by the lethal damage.

QIf this follower has 3 defense, then it takes 3 damage, can I search my deck for a Serpent Drake and summon it?

ANo. This follower's automatic ability would trigger, but it would no longer be on your field by the time you resolve the ability, as it was destroyed by the lethal damage.

QIf this follower has 3 defense, then it takes 2 damage, can I search my deck for a Serpent Drake and summon it?

AYes, you can.

QIf this follower takes damage during my opponent's turn, does its automatic ability trigger?

AYes, it does.