1985 coupe deville computer going?

I have a 1985 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?

Test the voltage on the battery should be 13.5 to 14.5 while running, any more than that will make the computer wig, any less might also. not normally though usually they can run fine down till like 10 volts. If its not this, replace the ecm, and keep the old one as an emergency spare. at least if it is not this you can now know it isnt!

good luck