Is there any way to trigger the rotation of some brush? It should rotate back to the first location after some time and be used as a door.

Doors in Nexuiz / Q3A can't rotate afaik.

You only can set speed and the amount of units that a door will slide in a given direction (left/right/up/down). But you can't make a door-brush rotate around an origin-brush for example.

For more infos on doors see the description of any func_door-entity that you have created by pressing "n" while your func_door-entity is selected in GTKRadiant.