Why would a/c vents be running when vehicle is off?
It has to have a source of power right. What's the source of power in car? Battery right. See if you can't connect the ac switch to I the ignition switch of car through the fuse. That's myadvise. Sounds more complicated then it really is.
That's seems impossible lol... But you should always turn the A/C off before turning the engine off...
if the a/c is off, then the only thing coming through is outside air.
Need more info ,,
What do you mean running. There may be some residual cool air but it should not be blowing the way it does when the motor is running.