After i bought all the bits you listed the seats wouldn't heat up and found out you also need an upgraded control module approx £100 ebay
which allows heated seats and also fitting of LED headlights if required ,the module is located under the the steering wheel to the right.
What I would do if I was you is ring Audi with your reg and they will tell you the part number for your car, I made the mistake of ringing them after I found out I'd bought the wrong one, but at least I know now.
It could be that part number or 8J2837015C , if it is the part ending with a "C" i have a brand new one for sale. You can check by phoning Audi and giving your car reg, they will tell you the correct part number.