so the earth rotates eastwards, sun move eastward and moon moves eastward, anything move westward in the sky ?

yes, Alex, even if you mean the rising and setting doesn't count. There are the well known retrograde motions between the stars some minor planets (asteroids) and the planets make, and comets can go also westwards for us.

people

The sun rises in the East and sets in the West as does the moon and the stars due to the rotation of the earth.

The International Space Station tends to move across the sky often in the opposite direction of the stars and planets, from the UK you can see it rise in the West and set in the East on the 2nd March at 18:42, it will be up for around 5 minutes.

The sun doesn't go west ward. it stays put.

http://www.socketsetsandmore.com/

Hold on.
It ALL moves westward.
Things rise east, set west.. hence moved from east to west.
There are no periodic exceptions to that rule no.
Shooting stars, debris fields, little bits of whatnots can go the "wrong way". but no.
The only thing that causes perceived motion across the sky in a given day (rather than a year) is the rotation of the Earth.

A few satellites in retrograde orbit