Hi I,m John I will help you with the fridge section freezing.
Yes it could be the thermostat , send me the model number I will look at the breakdown and get back to you.
The Model Number Is: ESS25LPGA WW
That model uses a temp sensor thats connected to the control board, replace the sensor it should fix the problem, heres a video on how to replace the sensor.
if you require more assistance let me know please.