1985 bmw Just shut off while driving and wont start

bad fuel shut solenoid

I suspect a clogged fuel filter. Having lived on bumpy rural roads for years, I has to change the filter on my '86 Sunbird 3 or 4 times.

According to the wiring diagram, there is no inertia switch on a Mazda MX-6. The fuel pump circuit only has a pump relay which is powered by a fuse and grounded by the computer.
And if the car did have an inertia switch it would not affect the ignition system.
If you have no spark and no fuel pressure I would check the circuits for the pump, coil, and computer at those fuse locations and beyond. Could have shaken something loose at the key switch or in the wiring.

each one of the cylinders have there own seperate coil, if cylinder 5 is misfiring then the coil is bad. One cylinder not firing will cause the vehicle to run really rough hope this is helpful

Coolant on the spark plugs is a classic indication of a failed cylinder head gasket. No point in doing any further analysis 'till you get that squared away. When you replace the head gaskets, it's always advisable to have the heads checked for cracks and warpage.

Does it happen when you accelerate and decelerate? If so, it might be a motor mount or transmission mount. If it only happens on bumpy roads, check to see of the battery is held down tight, otherwise I'm at a loss.

check the wires to the fuel pump if they have rubbed against something and the insulation wore through hitting bumps or rain could cause it to short and kick the relay and resets again and will start

Sounds like a bad computer>

This is not a sloution but i had a similar problem about 6months ago. I left the lights on which drained the battery, road assistant came to booost start it, there was power but no turn over, not even a clunk of the engine trying ( all electrics are working and lights in the dash are live), tried a new battery same situation,
I took it to BMW independant specialist who put it down to a ECU fault , i was duped into having a new key made as i had no spare as it was believed the immobilizer had locked the car up so to speak, this didnt work , so the mech ordered a new ecu, and had it reprogrammed and it turned over first time, It was bumpy idling at cold start cos i had my original dead battery but after a day it ran like it used to sweet as a nut.
it was expensive 500 quid to put right, but then you may have better luck with your mechanic.

the problem is your sensor is bad . the sensor for for the fuel pump is not sending power.