Yes. The words "sun, earth, and moon" are proper nouns when the sentence uses them in an astronomical context. However, "the sun is shining", should not be capitalised.
The moon that accompanies Earth is simply called "Moon" - note that it is written with a capital "M", since in this case it is used as a proper name.
Half the Moon is always lit, unless the Moon is eclipsed by the Earth.
The Moon is tidally locked to Earth; the Moon's "day" and the Moon's month are the same length. So the "near side" of the Moon always faces the Earth, and the "far side" always faces away from Earth.
some part of the earth ALWAYS faces the moon. ALWAYS (its a big ball we live on)
When you are referring to the Earth's Moon then it is always capitalized, if you are talking about the moon of another planet then it is not always capitalized.
Yes. The Moon's rotation on its axis is in sync with it's orbit around Earth. Therefore, the near side of the Moon is always facing Earth.
The moon orbits the Earth, so it is always visible from some point on Earth.
The moon that accompanies Earth is simply called "Moon" - note that it is written with a capital "M", since in this case it is used as a proper name.
Half of the moon is always lit by the sun, unless the sun is eclipsed by the Earth. The portion of the illuminated moon viewed from Earth depends on the moon's orbit. As the moon orbits, different portions of shadow and illumination are seen from Earth, creating the moon's phases.
What on earth (or rather the moon) is that supposed to mean?!
The Moon.
Because the moon turns as it goes around the Earth.