re: Barycenter Inside Planet Versus Outside
Yes, but the large body is still revolving around the barycenter. And the moon is still revolving around the barycenter, not the planet. It has the illusion of orbiting the planet, but that is only an illusion. It is really revolving around the barycenter.
And this is still true in the case of Pluto, where there is also the illusion of Charon orbiting Pluto even thou Charon is orbiting the barycenter.
I see no reason why the location of the barycenter between two bodies should determine whether or not one or both is a planet. The larger, more massive of the two should be considered the planet, and the lesser should be the moon, IMO. In all cases, the smaller body orbits the barycenter, not the larger body.
Oh well, it is not up to me.