Direction of the motion of stars with in Galaxy is same for all Galaxies?

All rotating objects rotate from west to east. That is the definition of west and east. North is defined as the pole from which the rotation appears to be anticlockwise. So your question should be, "Do the north poles of all galaxies point in the same direction?" The answer is, "No! The north poles of galaxies point in chaotic directions." Chaotic is not the same as random. There may be some correlation among neighboring galaxies, but on the grandest scale, the directions appear to be random.

No. In spiral or disk type galaxies the main mass of stars move in the same direction, and in a co-planar fashion, around a common center of mass. There would be exceptions where some of the stars or objects such as globular clusters have high inclination orbits that pass through the plane of the disk. Also most galaxies seem to have spherical halos that surround the disk of the galaxy. These halos contain much material and many objects that are gravitationally bound to the galaxy.

The "direction" of motion from one disk type galaxy to another is simply a matter of perspective. Viewed from the proper side they all can rotate clockwise.

Irregular and elliptical galaxies have poorly developed planes of rotation. The stars and other objects orbit the center of mass in many planes with orbital inclinations in all degrees.