WOW, that tranny SHOULD last FOREVER with a V-6 pushing it!
Anyway.....
Full automatic is if you are say driving at 55 mph and stomp down on the throttle. The trans should kick down to 2nd gear, and (with the V-6, slowly) GO. Same as if your doing 25 mph and are in 3rd, you stomp on it and it sould go down to 1st.
As for the coolers.....Next to your battery you should have two silver hard lines going into the side of your radiator tank. If all they do is this go in and back out to the transmission, then you haven't got a aux trans cooler. Believe it or not, my Big Block K3500 came just that way! No external cooler. I have the HD towing package and all! Anyway, if it has an aux cooler it will go from that radiator tank internal cooler to an external cooler out in FRONT of the radiator behind the grill. It will be about the size of a sheet of paper.
If you DON'T have one, then you NEED one to plow with, as if your engine coolant overheats, it will also not cool the tranny as well.