GET A NEW COOLER!!!!!!!!!!! the aftermarket ones are bigger and provide more cooling..(I always double up on them and put an electric fan on them also)...as far as a new converter I would look on jaspers web site and see what they say about it but I would bet you will have to buy one seperatly.....and yes the one you get will be a full rebuild

From Jaspers website listed as one of the updates for this trans:

3) The torque converter is remanufactured using a state-of-the-art
converter aligner/welder which holds converter runout to even tighter
tolerances than OE. This prevents pump bushing wear and front seal
leaks caused by converter vibration.

So it looks like it is included.