Emm... you select it and move it.
You do have both the platform and an origin brush (a brush with the origin texture) tied to the func_rotating, I suppose?
...and that's the bottom line because Mate de Vita said so.
No, func_door_rotating will stop spinning after it completes its path (in degrees - if it has a 1440 degree path, it will spin 4 times, then stop). A func_rotating should keep spinning until you deactivate it, unless you've done something weird with it.
...and that's the bottom line because Mate de Vita said so.