Question

Do all the stars in sky move? Why?

Answer 1

Yes they move.But which we see in everyday sky is the relative motion of them with respect to our frame as we are also spinning and moving around the sun.
Some stars have very less velocity too.

Thanks.
Tripathy.

Answer 2

the answer is yes. The stars are much much much farther away than any distance you can move on the Earth, so you shouldn't be able to see them "move" on the sky just by moving on the Earth.

One thing to keep in mind, however, is that the stars do move slowly over the course of the night. The entire sky rotates about the point in the sky where you can find the North Star. You should be able to observe this by looking up at a constellation early in the evening, and then looking for it again a few hours later. You should be able to see that it's moved.

It's important to keep in mind, however, that the stars aren't physically moving around the North Star. It's the Earth's rotation on its axis that causes this effect.