Afaik he defined the different frames of reference.
Yes it is revolving around its axis, that and the rest of the answers are to be found here: http://en.wikipedia.org/wiki/Sun
Actually, a rotating frame is non-inertial.
A rotating frame is defined in reference to an inertial frame of reference. Consider a beach ball spinning in my hand. which way is it spinning? If we judge it by comparison to me, it might be spinning, say, clockwise around the axis perpendicular to my hand. I'd we judge it in comparison to the sun, that answer changes.
I still think I'm right here, but welcome attempts to fix my faded memories of physics.
The direction of rotation is relative, but the fact that it is rotating is not. That is, an observer in the Sun's reference frame can, indeed, determine that the Sun is rotating. (The Coriolis effect is one example.)
The sun isn't taking me with it. I am also rotating around the milky way. I happen to be rather more acted upon by a big rock than either of those relationships, though.