For the airbag light situation to be resolved you need the airbag code to be deciphered from a scantool that can read airbag codes,,If the alternator has low output it would turn on also the ABS light,If the car was flooded it is posible that the control module did short out its location in in the center bottom console
Regarding the door. Ford used to use a microswitch buried in the door catch to signal when the door was fully closed Maladjustment of the door and/or striker often caused the striker to become damaged resulting in the failure of the striker to fully enter the door catch and activate the microswitch. They might still use that system.
Regarding the TPS system, it would be advisable to ask your local Ford dealer for a second opinion and a price quotation to fix it. I suggest you tell them nothing about what the tyre shop suggested might be the cause.
the car doesn't have any vibrations unless there is a problem
you can tell the accredited service center to run the fault codes and if nothing comes up walk away from the deal until the seller fixes the fault
How many miles on it? Coil-over-plugs and spark plugs may need changed. They can throw electrical interference which can put you in Fail-Safe mode. Happened to me.
If car has over 70K, change the Coil-over plugs and spark plugs. Don't forget to change a fuel filter every 30K also.
The light is on because something has malfunctioned in the transmission system, this can be a sensor or wiring or the transmission has a mechanical fault. The next step is to have a scanner hooked up and read the fault code that was set in the control modules memory when it turned on the warning light. This may require a trip to the local dealer.
Did you check the horn relay ?
The horn system consists of the following components:
horn switch (part of the driver air bag module)
The horn system consists of a relay, the steering wheel switch and 2 horns. The horns receive voltage from the switched side of the relay. The horn relay is controlled on its ground side by the steering wheel switch or the generic electronic module (GEM).
The horn relay is supplied with constant voltage from the battery junction box (BJB) on circuit 30-DA1 (RD).
The horn switch shares the clockspring with the air bag circuits, although each of these systems work completely independent of each other.
Inspection and Verification
Verify the customer concern.
Visually inspect for obvious signs of mechanical or electrical damage.
Visual Inspection Chart
Battery junction box (BJB) fuse 7 (40A)
Central junction box (CJB) fuse 33 (20A)
Generic electronic module (GEM)
If an obvious cause for an observed or reported concern is found, correct the cause (if possible) before proceeding to the next step.
If the concern is not visually evident, verify the symptom and GO to Symptom Chart .
A little white/blue smoke at startup is usually an indication of valve seals leaking a little. If it's only at startup and goes away, it's not a big problem - keep an eye on the oil level in the crankcase (dipstick).
If it's dense white smoke, and continues for up to a minute or so (or longer), you may be getting coolant into the cylinders - head gasket or worse problems. If this is the case, you may want to have it checked for contamination of the coolant by exhaust products.