What exactly does GP return?
It returns the position of the origin (center) of the sprite. By default the center is the top-left corner, but you can change it.
i reset the center of my sprite, and somehow my sprites position on screen changed too, what is the relationship between Center and Position of a sprite?
Because Position is the position of Center, if you move the center within the sprite, its visual position will change too.
and what does happen to the position if i rotate my sprite?
As I said, Position is the position of the Center. And Center is the center of all transformations, including rotation. So it will never change regarding rotation and scaling.