Re: Tanden Rotation
Well, I'm with Bob on this one. I do believe there is a clump of tissue that can move around and coordinate forces and movements across the whole body. But of course such tissue could not spin freely.
But, in terms of sensations or visualizations, that is a different matter that I would like to hear more about.
For instance, I heard Jack Wada sensei at Aikido of San Jose talk about a river under the ground, that is continuously flowing by. There is no river of course, but as a visulaization, I think it has some value in how it would affect your ki. You are supposed to sort of patch into the flow of the river during your movements. The visualization has ramifications for low power-sourcing, connection to the ground, and the sort of never-stagnant "to/fro" or "in/out" in your intent, which is something that I associate with unobstructed ki flow (to use a bit of traditional terms).
So, the free spinning in the belly may be a visualization trick. Or it may be an interpretation of a sensation.
On the other front, regarding what your sensei does and to what degree it is "internal." You have indicated his meditative/breathing practices that are some of the types that I think can indeed have demonstrable effects. So I would not be surprised if he has some kokyu and it can be expressed particularly well in certain techniques. But I think the stuff that is the subject matter of "Transparent Power" and "Hidden in Plain Sight" are more akin to the instant blanket-like domination you desribed in your push-hands experience. (although maybe even more extreme)
At any rate it sounds like he is pretty good, so I'll train hard and hope to be like him someday!