4. How do astronomers determine if stars are moving toward us or away from us?
The speed and direction of travel of a star can be determined by examining the Doppler shift associated with its movement. It's the same idea as when a car passes you while blowing its horn. The frequency of the horn increases as the car approaches you and decreases as the car moves away. By examining the shift in the light coming from star one can determine whether it's moving towards or away from us.
Damien Lemay photo