When coolant and or water gets introduced to an automatic transmission. It can and will cause failure. The material "clutches and bands" use as friction are attached by a water soluble glue. The glue dissolves and the transmission will no longer go into gear. It may happen fast are slowly over time.
The coolant leaks out.
It leaks coolant.
not always, but most times, yes. it will ruin the trans fluid pump.
Don't drive it! Have it towed to a garage that can flush the system, replace the radiator and hope that the transmission is not damaged.
You replace the radiator
Where is it leaking from? Could be front or rear seal or coolant lines Did you change gasket when you changed fluid?
How To Find & Fix Coolant Leaks http://www.aa1car.com/library/coolant_leaks.htm
Probably the thermostat is sticking.
First undo them at the radiator, then follow them to the transmission and remove there. After fitting new ones,check for leaks then fill trans fluid to required level.
No. Transmission fluid lubricates the transmission. Coolant is used by the radiator to cool the engine.
Coolant should not be leaking from your transmission the only fluid in your transmission is transmission fluid. A faulty transmission seal can allow transmission fluid to leak out.
Only if the sensor is malfunctioning.