The control-change effect has no duration. It will last until the game ends or the affected creature leaves the battlefield. It may be superseded by a later control-change effect.

For the third ability, if the player is an illegal target when the ability tries to resolve, the ability doesn't resolve and none of its effects will happen. No damage will be dealt, no cards will be discarded, and no permanents will be sacrificed.

If the damage from Nicol Bolas's third ability is prevented or redirected, the rest of the effect will still happen. Specifically, the number of cards discarded and permanents sacrificed isn't tied to the amount of damage dealt.