Bypassing AMD Radeon GPU of 27" iMac (mid 2011) for Target Display Mode purposes
Answers to your questions as asked are:


I've seen your model iMacs used in Target Display Mode regardless of the fact the GPU is playing up, so from that perspective you'll be fine.
N/A see 1 above.
Getting past the first two is the easier part, it's getting the iMac to go into TDM that's going to be your issue as you really need to at least have it booted up to the login screen.


For more general info on TDM refer to: Use your iMac as a display with Target Display Mode.