I'd do the simple things first to correct the engine problems. Fuel filter, air fiter, PCV valve, a treatment with "Techron" (that's a fuel system cleaner). Maybe a tune-up. Worst comes to worst take it to Ford and see.
But there are several postings on that subject here.
About the door. I just replaced the cable in the door for mine. It wasn't hard to open, the cable just snapped.
Your's may be broken. It's a pain to fix, but involves taking the door panel off, the foam sound sealer is then removed and you'll see the door handle. There are two screws that hold it to the metal part of the door, unscrew them and PULL the handle off (feels like it won't come, but it will) and you'll see the wire. It's surrounded by a plastic shield. It's designed to run in that shield, and if for some reason your's is broken it would be very hard to open.
Now it also may be the lock mechanism is in need of repair.
It's fun stuff, and if you've got the skills and time, go ahead. If not, that's another reason to go to Ford.
Hope it helps, and welcome aboard!
Nate