Cliffside Market

The control-change effect has no duration. For each permanent, it will last until the game ends or the permanent leaves the battlefield. It will override all previous control-change effects for those permanents, and may be overridden by a later control-change effect.

Both permanents targeted by the chaos ability may be controlled by the same player. If they are, the effect nothing.

If an ability of a plane refers to "you," it's referring to whoever the plane's controller is at the time, not to the player that started the game with that plane card in their deck. Many abilities of plane cards affect all players, while many others affect only the planar controller, so read each ability carefully.

Neither permanent you target with the chaos ability needs to be one you control.

If either permanent targeted by the chaos ability is an illegal target by the time the ability resolves, the exchange doesn't happen. If both targets become illegal, the ability doesn't resolve.

A face-up plane card that's turned face down becomes a new object with no relation to its previous existence. In particular, it loses all counters it may have had.