The control-change effect of Kefnet's Last Word lasts indefinitely. It doesn't wear off during the cleanup step.

If the target permanent is an illegal target by the time Kefnet's Last Word resolves, the entire spell is countered. Your lands will untap during your next untap step as normal.

Gaining control of a creature doesn't cause you to gain control of any Auras or Equipment attached to it. They'll remain attached, but an Aura's effect that affects "you" still affects its controller rather than you, the controller of an Equipment can move it during his or her next main phase, and so on.

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well, and any effects that give the player control of permanents immediately end.

No lands that you control will untap during your next untap step, even lands that aren't tapped as this spell resolves. This includes lands that enter the battlefield after this spell resolves.

If more than one spell says that lands you control don't untap during your next untap step, the effects will all wear off during that untap step. You'll untap lands you control during your untap step after that one.