Now if the star that emitted the photon were traveling AWAY from Earth at 1 x 106 m/s, how much FARTHER from Earth would the star be after one second?

Answer 1

You could also phrase this question as How far does the star travel in one second?

The question states that the star is traveling 1 x 10⁶ m every second (meaning of m/s = meters per second, where the word "per" means "for each" or "for every")

the question is not asking how far from earth is the star, it is asking how much the distance has changed.