The buzzing gearknob can be sorted, but usually means replacing bushes, clips, etc, even the knob itself. If it feels sloppy, best replace the gear linkage bushes and/or the linkrods/pins. Not a bad job to do actually.
The running on... this is a weird one... I have never heard of an E30 M3 running on. But, I suppose it could if it had an air leak on the Throttle body blocks causing high combustion chamber temperatures..... leading to hot carbon deposits in the head.... leading to your running on problem, also possibly causing your "over fueling" problems.
Other than that, there are several other things which can cause your flat spots. Its best to put the car on a rolling road with an oscilloscope connected to the ignition system, a CO/HC emission tester up the exhaust and a couple of runs on the dyno while all thats connected.
Other things to check are HT leads are fully home inside the dissy cap. Check the cap for cracks, damage and all electrodes inside the cap are in good condition. Also while there, check the rotor arm for cracks, etc. Put an ohms meter across the rotor arm (middle to end of metal contact and see what the reading is. There should be a resistance, but not too high. I will need to check what it should be, but if you have a reading of infinity, althought the car will still run, it can cause the problems you describe.
AFM (Air flow meter) do wear and cause problems, Also, the blue temp sensor in the water rail above the exhaust can cause similar problems too.
What temperature does the engine run at when running normally? If just below the half way mark on the gauge, as long as the black temp sensor is in good condition, this is fine. If it stays around the 1/4 mark or lower, this is running too cold... again assuming the black temp sensor is good. The blue sensor is what gives the ECU engine temperature info. The black one does the gauge.
But a dyno run will show everything up. These engines and you E28 M5 benefit greatly to a full ignition timing and fueling remap with the AFM removed. And if all the above doesn't help the running on, then I think the head would need to come off, decoke and modify the head ports while you're there
As to the ignition timing being out, unless there is interferrance to the 2 crank sensors or the ECU, the timing will not be out. It is ECU controlled.
Paul.
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