New to Bimmerfest/Buying a M3 in the near future

Im looking at buying a used M3 05-07 with about 60k miles on it. Here are my concerns if yall have any tips or experience please reply.

1. 50-60k Miles. Should i buy a BMW ext warranty or third party
2. Any major issues with M3 Convertible Tops? Years 05-07? I noticed there are more for sale than hard tops.
3. Is a used dealer really going to let me take a car off the lot to get it inspected buy my shop of choice? Has anyone ever done this? What was your method because i want to use this as a bargin tool also. I called several Indy shops and the Inspection II w/valve varies. Some also said if its not needed they will check for it but not actually do the adjustment.