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The door ajar and interior light problem is caused by a sticking dor ajar switch in one of the door latches. This will be difficult to diagnose without the Ford scan tool so what you can so is spray WD 40 inside the door latches and close/open the door 20 times. This will usually free up a stuck switch. For the a/c problem first run the self test on the system to see if you have a problem with the temp blend door motor. Press and hold the OFF and FLOOR buttons at the same time then release both and hit the AUTO button. You may see a code 24 or 25 diplayed in the panel.
Richard was right on with his answer on the door switch. I t took me five minutes to corredt the problem. I still have not tried to correct problem two, but the wife has not complained about the a/c either. Hope to look at that this weekend when the car is home for a few minutes.