Bit of bad news for you; middle seat on the middle row would be near impossible to extract by itself. The seat back may be able to be removed, but the bottom portion is integrated onto a bench-type assembly that the outer seats rely on. Unless you plan on some serious fabrication, I would look into mounting a cooler elsewhere, like in the driver's console.
As for modifying the third row, There's a picture on my Facebook page that shows the seat with the skin off. It's pretty much just a stamped steel backplate and foam, but I think you may be limited to what you can trim off by the latch mechanism that holds the seat up while driving, or in the event of a crash. Would be cool if someone could engineer fold-flat jump seats to go back there.
06 QT1, RC 2" Lift, 1.25" Wheel Spacers, 275/60/17 Hankook Ventus RH06 Tires, 20% Front Window Tint, Tinted Taillights and Front Turn Signals, DDM 6K HID lights, E&G Classics Grille, Debadged front, 1948 Studebaker 'Commander' Emblem Rear, Canvas/Slate Katzkin's Leather, Heated Front and Second Row Seats, CH-4100 4.5" DVD/NAV/iPod Headunit, 9" TView Rear Flip-Down Monitor, Accelvision RVC1100 Back-up Camera
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