You ask hard questions and are very adept at using so I wonder if I'm wasting your time but here goes.
a. From what I can find out the genius bars have a program/device that can tell if it qualifies
b. I would think not-- I believe it will need to either have the GPU replaced or ball grid reflowed
c. This is one company I found on the net that seems to have a good reputation but I can't swear to it.
http://www.etech-web.com/bga_reballing.htm
Good luck with this. Ralph