Abstruse Appropriation

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

Abstruse Appropriation doesn't change when you can cast the exiled card. For example, if you exile a creature card without flash, you can cast it only during your main phase when the stack is empty.

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.

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.

If a token is exiled this way, it will cease to exist and won't return to the battlefield. You can't cast it.

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If you leave the game, any spells or permanents you control from Abstruse Appropriation's effect are exiled, and any cards still exiled by it remain exiled.

In the rare case where the exiled card is a land card (probably because that land became a copy of a permanent while it was still on the battlefield), you won't be able to play it from exile.

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.