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I will answer your first question in two parts. Part 1 - For new boiler and pressure vessel construction, it is required to use material that has been endorsed by Section II of the ASME Boiler and Pressure Vessel Committee. I would refer you to Appendix A in Section II which lists substitution between A and SA material - A 106 can be used under the 1995 Edition of the ASTM specification. Otherwise, you must generate a Code case for particular usage of material, that is not listed in Section II or in Appendix A.
Part 2 - For B31.1 Power Piping, refer to paragraph D) of 123.1.2 -..Materials conforming to ASME SA or SB can be used interchangeably with material specified in ASTM A or B specifications of the same number.... with the exception of 123.2.2. In this section, if the piping falls under Boiler External the administrative rules of Section I apply - refer to Part 1 answer.
The ASTM committees have worked very closely with ASME B&PV committees over the years. All SA material originated from ASTM -A specifications. However, it is important to note that there can be technical or editorial variations that result in material having the SA designation versus the A designation from ASTM.
To answer your second question. ANSI is an accrediting organization, and I believe as publications are reviewed and approved by ANSI, they become ANSI publications, as well. Someone may add additional information.