does my mom's car have a dead short, sensor, or relay, or some kind of electric

Your warning lights may come on because of a vehicle stall. I do not think a low oil or low fuel concern is what you are experiencing. My gut feeling is that you could have a fuel supply issue. But a test will give you all the answers -- fuel pressure test at the fuel rail, check for any bleed down. The reason it may worsen with a lower fuel level is that with a lower fuel level, the fuel can heat faster and stay hotter longer. With heat comes reduced electrical pump performance if it is weak. Good luck with your Mom and cancer; hopefully you will resolve the car issue quickly so you can take this off her plate.