1985 coupe deville computer going?

I have a 1985 cadillac coupe deville. Recently when I started it up I noticed that the electronic gas gauge read that I was on “E.” I knew I had about 7 or 8 gallons in tank. I drove it around, and slowly the fuel started rising. I went to gas station and filled tank. It read “F” then quickly went to 15 gallons. (I believe it holds 18) Anyway, next morning I started car and since it was chilly, I adjusted temperature. Suddenly all lights on dash board came on/stayed on. Battery light, service light maintenance required, etc. Car then went dead. Restarted OK. I just ran the car for about 10 mins. all seems fine. Do think computer system is wigging out? Tune-up required, alternator going?
This is not my primary car. And since its almost 20 yrs old. I don't want to waste time and money. And certainly don't want car to just decide to shut down next time out. Any ideas?

Bad alternators and batteries make the electronics do weird things. Try testing the battery voltage with a volt meter while the car is off and running.