On many cars there is a control module installed in the door just behind the door panel.
Generally this module controls all of the items that you mentiond and a host of other items, now its possible that when the door got crunched the module was damaged in some way and now it is operating erratically.
You say that the places ( i think you mean auto repair shops ) there are shady compared to the shops in connecticut,,im guessin that ct. has its share of shady places too.
Have you considered the Ford Dealer ?
The Ford Dealers in D.C adhere to the same service and repair procedures as the ford dealers in CT.
Plus They both use the same parts and the same if not comparable warranties.
Also many dealers have onsite body shops too, so you can get the dent fixed at the same time if you wish or you can schedule the repair for a follow up visit.