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

When you cast Titans' Vanguard, its triggered ability will resolve before Titans' Vanguard does. If Titans' Vanguard is countered or otherwise leaves the stack in response to that triggered ability, the triggered ability will still resolve as normal.

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.

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

Since Titans' Vanguard's triggered ability resolves before Titans' Vanguard does, it won't be on the battlefield when that ability resolves, and it won't receive a +1/+1 counter.

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.

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.