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Anelastic or compressible or boussinesq?

Dear WRF experts/ users,
I had a few questions about the idealized 2D hill case and em_les case.
Q1. In the idealized 2D hill case, is there a way to find out if the momentum incorporates the anelastic or Boussinesq assumptions?

Q2. In the idealized em_les case, is it the full compressible Navier Stokes equations being solved or is it the anelastic case?

Q3. With regard to the runtime hydrostatic option in the2d hill case or other cases, what does it specifically do? What terms does it add to the hydrostatic relationship in the w momentum equation?
Please see my answers below:
(1) I don't think the anelastic or Boussinesq assumptions are employed in the ideal 2D hill case
(2) the full compressible equations are solved in the em_les case
(3) regarding the hydrostatic option, the document here describes in detail how the model handles this option.