How does aperture size effect barrel distortion and chromatic aberration? Why?

I'm pretty sure that aperture does not affect distortion, but it does affect vignetting, resolution, diffraction, and on some lenses, the degree of color fringing or c.a. Probably need an optical engineer to tell you why.

If the lens has internal floating elements, then focus effects the degree of linear distrotion, IE, the lens focuses at infinity has some barreling, and focused up close would have more barreling.