ABIs specify which registers are caller-saved and which ones are callee-saved. Since NVIDIA’s ABI for the GPU is not public (NVIDIA may share it under NDA with partners in addition to using it internally, but I do not know one way or the other), I do not have that information. You could reverse engineer most of it if you really needed it. What are you trying to accomplish that requires this information?
I do not know how the device-side linker handles functions with different register requirements. I think I knew some basics at one time, but since I have not needed that information for 10+ years, I cannot recall anything about this topic. Why do you need to know?