Bill Tindall, E.Tn.
An ax is something I enjoy swinging. I will use my favorite double bit instead of the chain saw for limbing or whacking 6" and less trees.

A file is an effective way to shape an ax head. Angle grinder works if there is major shaping to be done, then refine with a file. The bevel is convex and the angle depends on the use.

I usually polish the face with a fine India stone. I don't see buffing to be any use for an ax.

Lenoard Lee's sharpening book has an extensive discussion of axes.