You choose whether or not to cast the exiled card as Bismuth Mindrender's triggered ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.

If a spell you cast this way has {X} in its mana cost, you must choose 0 as the value of X when casting it.

If you cast a spell for another cost "rather than paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the spell has any mandatory additional costs, those must be paid to cast it.

If you choose not to cast the card, it remains in exile.

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.