Do the colors of the Galaxy related to its shape?

Sometimes. As a general rule one says that spiral galaxies are blue and elliptical galaxies are red. This is as spiral galaxies contain young stars and also constantly produce new ones. Older stars on the other hand have a reddish colour, causing the overall colour in elliptical galaxies. read more

The “colors” of any Galaxy has more to do with the ages of its constituent stars - with older populations of stars decidedly more reddish, and newer stars more bluish. Dust content of galaxies vary widely and can affect star formation. read more

The color of a few galaxies is affected by distance; an extremely distant galaxy has a high recessional velocity due to the expansion of the universe, which causes its light to be shifted toward the red (google "relativistic Doppler shift"). Most galaxies distant enough for this to have a noticable effect on the color of an image are very faint. read more