Most of the parameters are calculated with proj_factors(). See Map Projections - A Working Manual. Snyder 1987 for details.

The partial derivatives ∂x/∂λ, ∂x/∂φ, ∂y/∂φ, ∂y/∂φ are computed for an sphere or ellipsoid with a=1.

The "Elevation Scale Factor" is computed as Ra/(Ra + h) being Ra the Gaussian radius at that latitude and h the ellipsoidal height. The "Combined Scale Factor" is computed only when h and k are almost equal.

Selecting a vertical CRS that has a geoid model in PROJ-data will convert those orthometric heights into ellipsoidal heights if inputs are in Easting/Northing or N/E. This is useful only if you care about the "Elevation Scale Factor". Input in Lat/Lot are always with ellipsoidal heights.

You can also use projections from PROJ in the "Free Text" mode.