Why do clouds usually move from East to West?

That's the way the earth rotates, and it takes the winds with it.

Not sure what you are referring to. Low pressure systems move from East to West in the low latitudes and the polar latitudes. In the middle latitudes where most people live, they move from West to the East. This is due to global wind belts. There are regional effects too though because air moves toward the center of low pressure.

Clouds will move east to west when the wind is blowing from the east to the west.

Only if there is an easterly wind.