Mutated Cultist's triggered ability will resolve before Mutated Cultist does. If Mutated Cultist is countered or otherwise leaves the stack in response to that triggered ability, the triggered ability will still resolve as normal.

The triggered ability can target a permanent controlled by any player, but it can't target you. It can target a permanent or opponent with no counters. If the targeted permanent or opponent has more than one kind of counter, you must remove all of them.

Counters that players could have include energy counters, experience counters, poison counters, rad counters, and ticket counters.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions (such as that of Mutated Cultist's second ability). The mana value of the spell remains unchanged, no matter what the total cost to cast it was.

A card with devoid is just colorless. It's not colorless and the colors of mana in its mana cost.

Other cards and abilities can give a card with devoid a color. If that happens, it's just the new color, not that color and colorless.

Devoid works in all zones, not just on the battlefield.

If a card loses devoid, it will still be colorless. This is because effects that change an object's color (like the one created by devoid) are considered before the object loses devoid.

Devoid doesn't affect the color identity of the card for the purposes of the Commander variant. For example, while Abstruse Appropriation is colorless because it has devoid, its color identity is still white and black, and it can't be included in a Commander deck where the commander's color identity doesn't include both white and black.