QIf I attack a 0-attack enemy follower with this follower, do I still draw 2 cards?

ANo. When a follower with 0 or less attack deals attack or combat damage, it doesn't count as dealing damage.

QIf this follower takes damage that brings it to 0 defense or less during my turn, do I still draw 2 cards?

AYes, as long as it's the first time this follower has taken damage this turn.