2016 Explorer Limited 2.3L Ecoboost transmission 6F35 questions

[Srallen4]

I was having some battery issues then all of a sudden my over temp light came on as soon as I started it. It had been sitting for at least 4 hours on a semi cool day. I went to the gas station and got a little coolant, but it wasn't very low, so I barely added any. I let it sit for about 30 minutes after that. Drove the rest of the way home and light still on. Let it sit for maybe 5 minutes, and husband said it wasn't very hot at all let alone to be reading over temp. Then the battery started having more issues. Had to replace it, but it sat for 2 days under a carport with no battery in it. Got the new battery put in and was starting the reset process. The over temp light was still on. Drove 15 miles and stopped to check it, but still wasn't actually very hot or showing signs of overheating. Put some transmission fluid in it as it had been slipping a little. Got it home, and it died about 3 blocks and wouldn't start. Had the Check engine light on at this point. Towed it to the house and it sat again for a few days. Drained the transmission fluid and it was black with a slight burnt smell. Found out the husband put the wrong fluid in for about 10 miles of the drive. After draining it, put the right fluid in and it would not move when in gear. Let it sit a few days and it finally let me move about 15 ft to park it in a better spot. Figured out that my husband overfilled it, as he didn't realize it said dry Drained the fluid again and black with burnt smell. Over temp light is still on but it doesn't feel like its over temp. Can't see the temp gage as the light will not disappear to read the gauge. Any ideas? Or is it just shot! Any ideas would be useful. Was going to drain and flush the coolant system to make sure the right stuff is there. Already drained the transmission fluid, but was waiting to see if it was worth putting new correct amount in or if its just toast.

 

[peterk9]

Welcome to the Forum.
It's always to diagnose an issue over the Internet but is it possible that your thermostat is not working properly? I don't see a connection between the overheating, battery and transmission. How many miles are on the vehicle?
You start out by mentioning that you added some coolant, then had battery issues. What kind of issues? Then the next thing going on is adding transmission fluid. What prompted that?

Peter