If rigid supports are to be selected what are the load cases to be applied?
I guess you mean limit stop as rigid support, no spl load case is required...

What are the stress verifications that I should check?
Apart from SUS+F1 code stress combination, the flange check at PSV inlet flange and outlet flange plays a major role.

add rigid support that solve the reaction forccs but make worst the thermal analysis of the system.
Unless the layout is seen, the reason for high thermal load cannot be envisaged.