A1： it is the same as n2cosθ2/n1cosθ1. However it uses theta1 instead of theta2. You can deduct this formula with only theta1 with Snell’s law.
A2: Stack function can deal with dispersive material. Please refer to this: https://optics.ansys.com/hc/en-us/articles/360034406254-stackrt-Script-command
for RCWA, it is designed for periodic nano structure, and you may need to test how many k vectors are to be used in general.
For planar structure like thin films, in principle both should give the same result, with minor difference due to the fact: STACK is analytical without meshing whereas RCWA is semianalytical which needs meshing. The difference might be from meshing.
A3: I guess you uploaded the wrong images.
RCWA needs converging tests for mesh and k vectors in general, provided that the material model is exactly the same. Please note that STACK uses FDTD fitted material data. RCWA is frequency-domain solver so it might simply use the material raw data if you do not set the fit:
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