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

If the target of Thief of Existence's triggered ability is illegal as the ability tries to resolve, it won't resolve and none of its effects will happen. Thief of Existence won't gain another ability.

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.