1) Engine is a 1st Generation 5S-FE. 2) Heater (Core) Hose. Use drivers or passengers side when giving descriptions, makes it easier. 3) Cooked the oil due to the transmission cooler not having coolant. 4) Burnt the oil, overheated when lost coolant. Radiator coolant is used to cool transmission fluid. I would suggest talking to car to an automatic transmissions specialist or mechanic ASAP, so they can physically have a look. From the info you have given me above is what I believe has happend, but you never know until you actually take a look for yourself.