How are AVX registers handled by the common calling conventions?
The answer to both of your questions (assuming that you're talking about calling convention in C++) is in the great optimization guide by Agner Fog:
Calling conventions for different C++ compilers and operating systems.
See section 6 (Register usage) on page 10. Also section 7.2 (Passing and returning SIMD types) on page 22 might be relevant.