Gaining control of Contested War Zone doesn’t cause it to tap or untap.

The word “you” in a permanent’s trigger condition always refers to the permanent’s current controller.

In some multiplayer formats, creatures controlled by different players may deal combat damage to you simultaneously. If this happens, you control each triggered ability and can put them on the stack in any order. The last ability to resolve will determine who ends up controlling Contested War Zone.

The last activated ability affects all attacking creatures, not just those you control.