Question

Why pole appear to be stationary at night while other stars appear to move from east to west?

Answer 1

The polar star is approximately aligned with the Earth's axis of rotation, its apparent position is close to the celestial North pole, and lies approximately directly overhead when viewed from the Earth's North Pole. The current polar star is Polaris also known as the North Star.
If you project a line through the earth's rotational axis and out into space it will eventually pass close to (but not exactly hit) Polaris, the pole star.

The earth's axis always tilts in the same direction while it orbits around the sun. Only a phenomena called the precession of the equinoxes changes the direction of the earth's axis but that takes 25,000 years to complete a full cycle. It is always happening but very very slowly.