ELEMENTAL BACKLASH: Cosmic King can use Barrier. When Cosmic King is the target of a successful close combat attack, the attacker is dealt 1 damage after the attack resolves.

Question: if i use protected on the successful close combat attack the attacker is still dealt the 1 damage right? i think it's a pretty straightforward YES but i thought i'd ask. thanks!

That is correct.

Note that the attacker is only dealt 1 damage. It is worded more like Damage Shield than Mystics. It is not "takes 1 damage". So an attacker with Toughness or better can attack COsmic King with impunity (unless Cosmic King has Armor Piercing)