QWill this follower also deal 1 damage to itself with its Fanfare ability?

AYes, it will.

QIf I play Clash of Heroes and select this follower and a 0-attack enemy follower, do I still deal 1 damage to each enemy leader?

ANo. When an ability does 0 or less damage, no damage is dealt at all (it doesn't count as dealing damage).

QIf this follower takes ability damage that brings its defense to 0 during my turn, do I still deal 1 damage to each enemy leader?

AYes, you do.

QWhat is ability damage?

AAbility damage is all damage except for damage dealt by two followers in combat or by a follower attacking a leader. For example, if you deal 1 damage to a follower on your field with Disdainful Rending or Disciple of Disdain, that's ability damage.