I know there is a timed relay on the door locks that automatically locks them when you have used yoru remote to unlock them and never open the door or trunk. It takes about a minute before it does this. When the ignition is turned on however, this relay disables itself as the doors don't autolock after driving. It's probably a problem with this timed relay, but it is just a guess. I have no idea what it is called or where it may be located. Door definitely should not lock themselves when the vehcile is only running. My only other speculation is a possible short in your drivers door lock, which needs to be turned to disable the alarm when it sounds. Since you mentioned your alarm going off as well.
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96 850 GLT 5-Speed