Question

Does star change their position?

Answer 1

There are two things that are to be considered in change of change of stars position.

1. Movement of the stars
2. Movement of the earth

Movement of stars

As you might already know, nothing in our universe is stationary. Every celestial body is rotating or revolving, or both, around another body. Stars do the same.
If they are just rotating about their axis, it does not contribute much to their movement as observed from the earth. If on the other hand, it is revolving around an axis, it's movement is measurable, but it will be very small, depending upon how far the star is.
As most stars are very far away from earth, thier motion can't be detected by us.
Bernard's star, the 4th closest star from earth that is around 6 lightyears away, has the largest proper motion of 10.3 seconds of arc per year. At that rate, it would take it about 180 years to change it's position equivalent to the angular diameter of the moon. So as you can tell. Movement of stars does not play a major role in it. In fact, the position of stars as seen by Galilio is still the position of stars as seen by us.
The above motion of stars is called proper motion, which is the apparent angular motion of stars with respect to other stars.

Movement of earth

Our earth also rotates and revolutes around an axis. Because of this, stars appear to rise in the east and set in the west. In the north, some stars never rise or set. They are called circumpolar stars that follow a counter clockwise direction.( It is the centre of these stars is what we definite as north ).
So there you have it. What we see is just the effect of the earth's rotation.