What problem do i have with tmy 2002fairmontkeeps shutting down when leftfor a while after driving

Yes it will. Your having to depress the fuel pedal more and force more fuel into the engine. Eventually the engine will just stop running because the exhaust cannot get out.

run the fault codes and check for cam/crank position sensors
check for broken timing belt/chain
check immobiliser operation
check for problem ignition control module
if the timing belt has not been changed at 60000 miles or 100.000 klm s then it is a fair bet that it has broken

driving in over drive mode actually is what gives the economy as the engine rpms will be around 300 less than direct drive . Lower rpms = fuel savings
OD should come in around 60 klm/hr and drop out at around 50 klm/hr. When you are accelerating hold the pedal in a set position and watch the rev counter (rpms ) and each gear change you will see the rpms drop and then build back up as the vehicle speed increases At 100klm/hr the revs should be around 3200 rpms or less but if over ( say 3500 rpms) then may be the OD is not coming in. One way to test a box operation is to find a speed shop with a dynomometer and test the gear selections against loads and engine rpms

I would start with the cam and crank sensor first having them tested.Make sure it has a square wave completely threw its voltage cycle. some can break down at low rpm it is where they mostly run at. If this does not help Wheel sensors are another culprit also the IPS and OSS which is input speed sensor and output speed sensor is it a manual or automatic we need these type of details to assist you properly thanks in advance.

I am not familiar with the car, but is it a 4 wheel drive at all?

If it is and its engaged that can cause a shake like that.

I’m happy to assist further over the phone at https://www.6ya.com/expert/robert_54ae41aaaffbab00

Replace your MAF, its a little pricey around $280.00 or so but this will clear the code but make sure you have the ECM reprogrammed to perform a "learning" sequence since sometimes the code will not clear even though the vehicle will run like new. This reprogramming will most likely have to be a dealer performed procedure.

Well anything is possible, but I would expect the transmission to work given the time and mileage.
Is there any way you could drive it a short distance before spending much money ?
I am assuming you are having the fuel tank drained and the cooling system flushed among other things.
I would change the fluids and try to drive it a few blocks before spending money on much else to see what it will need.

Must have had water in the transmission. Not it's toast

I would not think so, the wire going to the hub is for a wheel speed sensor for the anti-lock braking system.

The only way to find out what the problem is is by doing a scan of the car computer module using an OBD code reader.
The codes returned will tell you the cause of the problem.