In the 2000 Kia SEPHIA, the door has two spring-loaded sensors that do not close all the time, causing the dome-light to stay lit all night. Also, I had to replce the alternater because it could not keep-up with the air-conditioner and the radio and day-time drive-lights at the same time. My clue was the check-engine-light and the over-drive light always on. At the end the parking-brake lights and then finaly the battery-light came on.
A raidator in need of a flush will not cause a battery drain.
A short in the wiring.
Shorted diodes in the alternator.
dead cell in the battery or something is on pulling power from the battery.
Your alternator could be bad.
Any relay could be the cause.
If no light is on and no relay is stuck then the battery has a dead cell and needs replacing.
I'd recommend you do a battery test and charging system test. The battery would be my first suspect.
Could be a shorted wire, or bad battery.
Good possibility
Yes possible. If switch does not open on engine shut down battery will drain If switch does not close on start up battery will not charge
Yes, if the relay was stuck it would drain the battery.