83 Cadillac stalling issue

Did the trans concern and the stall come on at the same time? It sounds like you possibly have two separate concerns. When the vehicle stalls, and won't start, pull a plug wire and check it for spark output. To do this, you want to use a screwdriver inserted in the plug end, hold it close(1/8 to 1/4") to an engine grounding point, and crank the engine. If you don't see a spark, or feel one as you will if your gap is too large, you have a no spark condition. I would initially suspect a faulty ignition module, with that result.

I also have pushed the Warmer and Off buttons on the climate control and it showed 4.8.8 and 7.0 codes and the service soon and service now warning lights came on at the same time. I can't seem to find any information on this in the Cadillac book.

I have had the fuel pump, fuel filter replaced. Had the spark plugs and wires and distributor cap replaced, and oil has been changed.

But have you checked it for spark when it won't start? You are losing something to cause it not to start.