https://repairpal.com/estimator?car_type_id=5255
Click on that link to our Estimator tool - and select "CV Boot Cover Replacement" to find the going price for your vehicle in your area....for the CV boot. Keep in mind also that many aftermarket part stores carry complete axle assemblies that could end up being a better value for you...and much less labor intensive, since no joint removal is necessary.
Regarding your engine shutting off - an Audi specialist is the best resource for your vehicle. A good diagnostic test with proper equipment and know how is in order for a vehicle as specialized as yours. Here is a link to some repair shops near you that will work on Audi's:
https://repairpal.com/directory?address=38104&car_brand_n...