Bought my 85 wagon out of a barn, was used in summers only. A year later, I have taken it from Maine to Florida and back. Only needed brakes & a good tune up. In FL had another tune up, fuel filter replaced, injectors cleaned. Coming back from FL last spring, fuel pump began making noise.
Just before heading south two weeks ago, replaced fuel pump and fuel pump relay(as a precaution) She started stalling and running rough when I first start out. When I first give it gas, YIKES, cough cough. As she starts going, it backfires (from underneath not out rear). On the highway she flies. Hit traffic and it stalls after a few minutes idling. Stopped and had the Master Air Flow and Catal. converter replaced (because mechanic said it was running rich (black spits out exhaust) and it seemed fine. Started south again. Again, died in traffic but loves the highway. In VA now, just had the fuel pressure regulator replaced. Idled well at garage pulled out into traffic and she now back fires, idles rough, and hardly moves at low speed, when speed increases, no problem. She is coughing and barely running now. Leaving VA in two days for Florida HELP . Don't want to pay someone a fortune for things it may not need, like I already did. HELP

 

Had a stalling problem made better by Fuel Pressure Regulator, stalling out while running. But idling was still giving my 1990 740 GLE some issues (though not as bad as yours):

check the PCV hose that leads from the air intake tube to a hole on the side of the crankcase. kind of hard to see under intake manifold. I've had idle issue with it occasionally stalling at a lights and this pulsing idle at rest. Was considering Idle Air Control Valve as culprit, but today I refit this PCV hose to seal better on crankcase (I found a replacement flange for the crankcase end: a flanged hose cut off an old BMW water pump, put a zip tie around it) and put some black silicone on inner 2" soft tube (it was crumbling in places), the issue seems to be solved. You might have other issues, like the Idle Air Valve, but this is much simpler to deal with first. Idle valve for mine (90 740 GLE) is running around $135 cheapest I can see on Amazon.

when you can, run a diagnostic check on it too.