Well, what it sounds like is that you got a leak between throttle body and maf, the leaked caused engine to think it was running lean so it added fuel to compensate for too much and not enough fuel. The extra fuel (which it didnt need) caused the catalyst to melt which restricts hot gases from leaving the engine and built up causing excess heat causing plastic to melt.
MAF and/or IAC (idle air control) may or may not have been bad considering how bad your condition was at the point of diagnosis, since Im not their I really dont know.
Now the transmission may have gone into fail safe mode or just lost an input like a sensor signal, and may not be related. Its possible a sensor wire may have been burn/damaged form excess heat off the exhaust, or during repair a sensor may have come disconnected. I would go over all the wire under the hood and car to see if their is loose or damaged. If your friend has a good scan tool he should be able to look at the transmisson to see whats going on.
Also the transmission most of the time does not set a cel as the cel is for emissions issues with the engine. Hope in some way this helps.