The second ability checks that the targeted creature is a Cleric or Wizard only at the time the ability is activated and at the time it resolves. It doesn’t check at the time the damage is actually prevented.

If you activate Wandering Mage’s third ability, you put the -1/-1 counter on a creature you control as a cost. That means it happens when you activate the ability, not when it resolves. If paying the cost causes the only creature you control to have 0 toughness, it’s put into the graveyard before you can pay the cost again.