SnTMan, As per UG 11(C), fittings under UG 16.9 are pressure parts that comply with ASME product standard accepted by reference in UG 44.
As per UG 5(C) pressure parts, such as standard pipe fittings, welding caps, and flanges that are seamless or fabricated by one of the welding processes...
Its an iterative method. The bolt size should be optimum for required cross-sectional area.In simple, If the bolt is too thin, it will not meet the required cross-sectional area of bolt & if it is too thick, Flange moment for Gasket seating condition may increase and you will get a thicker flange
You can refer Zick's method for calculating the effect of saddle support on vessel
Main stresses are Longitudinal bending, Circumferential and tangential shear. Longitudinal stress should be added with stress in longitudinal direction (girth seam) to get total stress in compression.
Regards
Jithin