"Anonymous. Rotate. To move in a circle round an axis."
Yes, however most dance actions comprise a rotation about an axis WITHIN the body, added to a linear translation.
"If I stood facing the centre with my partner to my right side but backing the centre. When I rotate clockwise where will my partner be.without moving her position or contact point. Then rotate the same distance anti-clockwise. Where is she now."
What you are describing would be a rotation around a common center outside of the bodies, which would require each dancer to move on a curved path. In fact, that is not what usually happens. Instead, we each rotate our own body.
Because we are also moving as we do this rotation, it may appear as if we are rotating around a common center, or about our own left elbow or something - but if you take into acount that varying distance from the supposed axis, you will see that it is not actually such a curved movement. Instead, it is a rotation about an internal axis, added to a linear travel.
"There will be no hip to hip if CBMP is applied correctly. Will there?"
No, the backward partner's right hip will stay in front of the forward partner's right hip, with respect to the direction of travel. The partners have STRETCHED past each other, by they have not actually passed each other.
Compare for example the first step of a feather step with the first step of a natural turn. They are actually very, very similar with only slight differences. Even in the natural turn, there is not passing of the partner that occurs on the first step - there is stretching past, but the actual passing is left for the second step. In a feather, we merely assume this stretched past position and hold it through step 2 where we call it side lead, and step 3, where we call it CBMP and outside partner.