The car may well be possessed, but I think that may be an aside from what's going on with it mechanically.
Lights? I'd start with a fuse check and a cleaning of the fuse panel - emery cloth all contact and make sure wiring harnesses for rear lights are giving a good contact.
Screaching? I think that's fairly common and harmless. Seems to mostly happen in cold temps. Probably related to bearings shrinking and oil thickening.
No/hard start? From what you describe it could be condensation in the tank which froz and then caused some clogging. Keeping tank at or near full will help prevent that. Throw some fuel line antifreeze the tank and give your daughter an extra bottle. Are you/she getting quality gas? If there's water in the gas...well, you know.
Tell your daughter if she talks to the car now and again it will not become possessed.