THE HEATER BLOWER MOTOR HAS STARTED RUNNING EVEN WHEN IT'S SWITCHED OFF

The climate control system should stop running when the vehicle is shut off as you know, so there must be some kind of failure with the module that controls the system still receiving the power necessary to keep it running. Failure, meaning, something is keeping it enabled. This will take professional testing with diagnostic equipment and wire testing.

It's pretty simple . Have your mechanic check with an oscilloscope for aberrations with the blower motor actually starting by itself. If it activates it will stay on for 20 minutes draining the battery. It is either a bad relay or bad blower motor. Nothing in your vehicle should start or activate by itself with the key out. After he repairs that have him let the car go to sleep for 20 minutes and put an oscilloscope on it and check for any other parasitic drain. Also have the mechanic check the TCM or Telephone Control Module & pull the fuse.