What failure modes and what loads are you assessing? Why would axisymmetric not be suitable here? This is a fairly simple model, why not just use solid elements?
What figure are you following? Typically a plate type flange is considered to be a loose type and the connected shell material is not considered to provide additional strength.
What are your units? millimeters? Differences in the realm of 1e-4 is pretty darn small and well below any reasonable manufacturing tolerance for a pressure vessel. If you are still concerned, you can run more increments to see if things change.
You are also using some pretty coarse tet...
Per U-1(e)(1)(-c) the scope of the code is up to the face of the first flange or bolted flange connection. The DIN flange is within the scope of ASME VIII-1 and as it is not an adopted standard, the flange must be designed in accordance with Appendix 2.
The code is pretty clear here. Look is ASME II-D Table 3 for material with an allowable stress that is equal to or greater than that of SA-193 B8 Cl. 2. If you can't find one than use SA-193 B8 Cl. 2.
i) I don't think you can eliminate the deficiency since it is a code requirement per UG-44(b)(3)
ii) Look in ASME II-D, Table 3 for a bolt material that has a higher allowable than that of SA-193 B8 Cl.2
Yes all of those software packages have a user manual. Since you have no experience, you should probably invest in some training to help.
What code of construction are you following for the design? Note that if you are working to ASME VIII-1 or ASME VIII-2, there are experience requirements...
CSA B51 paragraph J.8.1(d) requires "plot with element stress and a comparison of nodal (average stress vs. element (non-averaged) stress". Does anyone know how to create this plot in Ansys?
Since you've ruled out PVElite and Compress I am assuming you're working with ASME VIII-1. I think your only other option is DesignCalcs. There are some other fringe programs out there but I am not too familiar with them. You may need to develop your own spreadsheets to supplement any shortfalls...