The control-change effect has no duration. The targeted player retains control of Jinxed Idol until the game ends, Jinxed Idol leaves the battlefield, or an effect causes someone else to gain control of it (perhaps because Jinxed Idol’s ability is activated again).

If you sacrifice an attacking or blocking creature during the declare blockers step, it won’t deal combat damage. If you wait until the combat damage step, but that creature is dealt lethal damage, it’ll be destroyed before you get a chance to sacrifice it.

Your opponent can use the ability to give this card back to you.