Sunlight is actually mostly green/blue, more green at the surface. It just appears white because that’s what we’re used to and the difference in intensity isn’t that much for visible light anyways.

See https://seos-project.eu/earthspectra/images/Solar-spectrum.png

Rest checks out as far as I remember! Though the wording about the scattering is a bit loose. More specific details at https://en.wikipedia.org/wiki/Diffuse_sky_radiation