When started,I let idle to warm up but after 20 minutes notices it was not running and the serpentine belt snapped and coolant on floor.Please advise if it has an automatic shut off when over heating.

Hello, I'm not aware of any vehicle that has a feature where the engine will automatically shut off when overheating. I know that some engines "de-power" when overheating, but not shut off. Is it possible the charging system also failed causing the stall due to the belt failure? After all, you had a battery issue in the first place; a low battery and non-existent charging system probably caused the stall. Overheating isn't good, ever, but you can't assume other damage has occurred. Testing will be required to see what other concerns have happened.