Galaxy motion and distance are determined by a few different things, but the main one is red shift. When light moves away from us, the wavelength of the light gets stretched out, making it appear more red. This is known as red shift. By measuring the amount of red shift, scientists can determine how quickly a galaxy is moving away from us, which in turn tells us how far away it is.
Elliptical orbit and white dwarf are not directly related to determining galaxy motion and distance. Absolute magnitude is related to the brightness of stars, but not to galaxy motion and distance.