Transmission cooler, yes, it's right below the engine radiator. I haven't looked at the specs for the jag, but the LR3 is an SUV that weighs 6,000 lbs empty, and is designed to hold 7 adults and their gear. I think that would explain why the engines have been tuned differently than an aluminum sports sedan.....
I'm not to certain about the exhaust system, but this is what I think the bits and pieces are:
I think there are two catylic converters, one on each pipe, not far from the front row seating area (underneath, obviously). The dimpled canister and barrel cannisters after of that point are resonators, and the muffler is just forward of the dimpled canister.