[Dr Stig 2]

A/C.
Yes - it turns the engine back on to start up the compressor again if the temperature rises in the cabin. Possibly only matters in hot places where she heats up quicker. For heating in cold places, the residual heat in the radiators would do the job with the cabin ventilation without having to hit up the compressor of the A/C.

Getting out?
I have tested it. As soon as I open the door and move the key away from the proximity sensor with the start stop function having been activated, the car switches off the engine.
Haven't tested it exactly to see if it is the key moving away from the sensor or the actual door being opened that triggers it, but I imagine it is triggered by either of these events happening.