What is the flow direction of the transmision fluid through the radiator cooller. i.e. "hot" fluid gose in the top line,coolled oil gose back in the bottom?

I would say it is possible an overheated engine which is not coolling the transmission can trigger a lot of lights. Many transmissons are heated and coolled by a line which goes to the radiator of the engine cooling system.

most cooling systems are designed to have a 6 deg difference in temperature from the inlet to the radiator "hot coolant in" to the bottom hose of the system the "engine coolant feed. cooling systems are pressurerized to help the coolant carry the heat away from the hottest parts of the motor.
here are a few things to check check the rubber seal on the bottom of the radiator cap for tears uneven surfaces, ect if damaged replace it. your truck has a coolling fan this is called a clutch fan. these clutches can go bad and cause the air flow through the radiator to be comprimised by the slowing of the fan. you should be able to see if this is happening just by watching the fan to see that it is turning as fast as the motor.
then the 2 most common causes of over heating are a thermistat that is sticking or stuck. these are cheap parts and should be replaced as a matter of routine maintinance. i change mine every year its cheaper than getting a warped head from over heating. this is located on the engine end of the top radiator hose and is located inside the housing that is bolted to the block with 2 bolts.
check the back side of the oil filler cap that is located in your valve cover tanish to white collored sludge here will indicate water in the oil and point to a blown head gasket. also if you have any oil in the radiator.

sounds like you have damaged the transmission clutch pack.

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If it is trans fluid the cooler inside your radiator must have a leek. Yes it is possible for it to get itno the trans. Check to see if the fluid is milky.

Sounds like the thermostat is stuck open or fans running all the time (if electric). If water pump was shot, then engine would get hot, depending on the temperature where you are.
Electric fans, or belt powered? If electric, do fans run all the time? If so, replace the fan relay module, which are prone to failure in Chrysler products.

The heater core may be "plugged". Take both hoses off and using a garden water hose, see if you can get water to flow in and out of both hoses. If it flows slow or a lot of gunk comes out, its plugged, just keep reversing the water until it flows freely in both directions. Then hook up the hoses, top off the coolant and test drive it.

have u replaced the radiator and hoses? Thermostat could also be stuck open. Water pump could also be your issue. with motor cool and of remove radiator cap(cap may be bad as well) top-off fluid and start car check for fluid flow with flashlight. Water pumps typically leak from what is called a weep hole when the shaft seal fails. Yours will be located under the timing cover (drivers side) running of the timing belt.
Hit me up after u have check on these.

Flush cooling system , and get transmission flushed & fluid and filter changed as well. Then install new radiator. Hopefully you caught it before damage to transmission.

Check your fluid level. If a trany is over filled then the fluid will begin to foam and blow out of the vent once heated. Or you may have a overheating tranny. You can disconnect the tranny lines from the radiator and blow air through the fluid line ports on the radiator to make sure your not getting a plug. You can also purchase an external oil cooler to hook inline with the fluid ports on the radiator just make sure that when you install it to install it on the port that returns the fluid back to the tranny not the one that delivers the fluid to the radiator, in other words after the radiator not before.