1. The Sun is *moving* relative to it previous position,
There is no such thing as absolute motion. If we don't accelerate the sun, then I am at liberty to choose a coordinate system in which the sun is at rest. So no, the sun does not move, according to my choice of coordinate system...and your arguments have to work in that coordinate system.
No, you are not at liberty to change reality.
True, you can create a fictitional *model* in which the Sun and Earth do not "move", just as I could create a fictitious model for two cars that are both traveling together at 70 miles per hour, but it would be erroneous to say that simply because my *model* of those two cars had unchanging reference points that the cars weren't physically moving.