electrical problem

I have a 2002 Saturn SL1 with the 1.9L engine and I am having what appears to be an electrical problem. I replaced the battery about 3 weeks ago and everything was fine but now the electrical system seems to be unstable. The Gas gauge read zero and the lgas pump ight came on and the tank was about 3/4 full. The service engine soon light and service light were both on and the car would not start but the car would turn over. Came back later and the car started and all lights and the gauge were fine. Tonight the headlights went out and came right back on while driving down the road and then the interior lights didn't come on when I got out of the car but then came back on and the security system did not work. I turned the car off and then turned the key back on and the gas gauge and service engine soon light and service engine light both were on. The car did turn over and then finally started after the gas gauge went back up. All the lights went back to normal. Any suggestions?

Welcome to the forum. Get the codes read at autozone if you can and let us know.