Absolutely! In fact, since there is no rayleigh scattering (the phenomenon that makes the sky blue here on Earth) because the Moon has no atmosphere, you can see the stars ALL the time - even when the Sun is up.
Additionally, because there is no atmosphere, the stars appear brighter from the Moon than here on Earth. One of the major goals for a manned presence on the Moon will be to build lunar observatories. And because radio astronomy here on Earth is complicated by all the radio transmitters here, the PERFECT place for a radio telescope would be on the far side of the Moon. With several hundred miles of rock between the radio telescope and that horribly radio-noisy Earth, we'll be able to do radio-astronomy there far better than we ever can here on Earth.
Very little, the moon is too far away, on a good day you can just about make out the continents.
Shooting Stars and comets.
Stars
Yes, but not normally viewable to the naked eye. This is also true of Venus.
Because the Moon is much nearer than the stars to the Earth.
the moon and the stars are made out of moisture and dust
stars are galaxies away from us and the moon isn't
No, the moon is closer to Earth than the stars. The stars we see in the night sky are typically much farther away than the moon.
None. Stars do not orbit the moon. They are murch farther away and much larger than the moon is.
There are only 6,000 stars in the night sky which are viewable with the naked eye. But there are billions if not trillions of stars in the universe. Remember one star in every solar systen, millions to billions of stars in each galaxy, and billions of galaxies in the universe.
moon is too nearer to earth than stars
The moon and stars are both out at night.