Question

Why are there no stars in the photos of Earth taken from space and from the Moon?

Answer 1

Brightness

Explanation:

To get a decent exposure of a bright object against an almost totally black background, you have to either take a vary fast shot (low exposure) or lower the quantity of light coming into the camera (high aperture). In either case, the light of the stars would not register enough on the film to appear on the photos (or in modern cameras on the CCD).
Conversely, if you wanted the stars to be there, the earth would almost look like the sun in your photo.