To answer your first question, you need to obtain a copy of ASME Boiler and Pressure Vessel Code, Section IX. The Table in QW-422 provides a comprehensive listing of all accepted P-No, Group No materials. The assignment of P-No and Group No is based on weldability characteristics and mechanical properties of the various base metals.
ASTM – the American Society for Testing and Materials is a scientific and technical organization formed in 1898 for the development of standards on characteristics and performance of materials and services. ASTM is the world’s largest source of voluntary consensus standards.
API - American Petroleum Institute is an organization that develops specific Standards for various industries. They assign material designations based on their own criteria for materials application.