Strange Heating and A/C issues. Car possibly haunted.

I'm absolutely baffled about my car's heating/cooling issues so maybe one of you can
help. I'm not sure if the two issues are related or not. I bought my car in 2011 and the
dealer told me up front that the A/C did not work but the heat was fine. After a year I
started having a strange issue when I used the heat. If I turn the heat on while idling
the engine rumbles and eventually will stall out. As long as I turn on the heat while
accelerating I don't have any issues even when I'm stopped. I've had the heating issue
checked out and no one could explain it fully. I've been told it may be an air intake
problem but when I've changed my air filter the issue continues.  The A/C issue is that
it has not worked since I bought the car. An oil change shop did a diagnostic and they
thought that it was an issue with the compressor since the freon was fully charged.
I've turned on the air for circulation many times and there has never even been a hint
of cool air in four years of owning this car. I finally saved up enough to have the A/C
fixed and decided to take it to the mechanic today. The A/C started working without
the mechanic touching anything! After explaining both the A/C and heating issues to
the mechanic he could not thinking of any specific reasons these issues would
happen.
Any ideas on what could be happening here?