Typically, IBC building codes will reference ASCE 7 in one of it's incarnations (see the building code, chapter 35, to determine which). ASCE 7 will get you the total seismic load, but won't necessarily tell you how to apply it to the vessel. Vessels are "non-building structures not similar to buildings", usually.
Not all vessels are in USA and ASCE does not apply. Calculation of the EQ load static acceleration we can local EQ codes.
We are looking for guidelines of how to correctly combine the EQ reactions with other loads and what stress category this combination is. ASME 1 is very brief on this, ASME VIII has more detail. Are the combinations and allowable stresses the same for the vessel shell and nozzle loads?
The ASME codes are allowable stress, however many building codes now calculate ultimate strength seismic. If your local code does this then the ultimate strength seismic should be factored down so your vessel isn't overdesigned for seismic. ASCE 7 clause 2.4.1 uses a factor of 0.7 to do this for their seismic
Not familiar with ASME 1 so I can't help with that question.
I am not aware of seismic guidelines for the construction of fired and unfired pressure vessels but there will be guidelines for the supporting structures of these vessels and for the piping connected to such vessels. Take a look at API 650, 11 edition, Appendix E as there is seismic guidelines for vertical storage tanks and that Appendix E a bit more complicated than the second paper in MJCronin's reply . That second paper by MJC is also presented in the Pressure Vessel Design handbook by Bednar which is for tall vessel and I surmise can be adapted to multi story power plants. I suspect that if ASME adopts seismic guidelines it will follow a parallel line to API 650, Appendix E.