Q: Battery light came on while driving and a day later vehicle overheated

I was driving my vehicle and I didn't allow it to warm up but I sat after starting it up for 5 mins and I then pulled off i cut on my DVD player and then started to cut my heat in and my battery light came on and my steering wheel started to get tight. And then I cut the heat back off and the battery light went off. The Next day I drove it and the same thing the battery light came on but I realized I didn't have any engine oil or coolant at all I filled the engine oil and coolant up and then let that ran threw and it cut on again and stayed on for a few seconds and cut back off while in front of autozone they checked the battery and starter and alternator and he said they passed he also stated that the batter I had was smaller for my vehicle. So while driving home I cut on the heater and it was blowing out cool air and was getting colder as I was driving so I cut it off and soon as I cut the heater off the temperature was still normal and in 2 seconds the temperature needle went to h

My car has 188000 miles.
My car has an automatic transmission.