The moon appears to be a nearly perfect counterpart to the sun.
They appear to be about the same size as one another and about the same distance from the earth.
If the sun is a big ball of fire, than perhaps the moon is a big ball of ice.
Does the moon emit its own light?
Does lunar light cool as sunlight warms?
The moon has a face just as earth is said to have a face when viewing it from space.
The moon has two primary colors, dark grey and white.
Perhaps the dark grey color represents liquid and one material and the white color a solid and another material, or vice versa.
Sometimes the moon changes color, occasionally it's red, blue or golden.
I wonder what these color changes represent?
Maybe the lunar weather is changing, or vegetation on the moon periodically goes through metamorphosis.
I would assume from your questions that you are either lacking in education at this time of you life due to a young age, or are not widely experienced in observation etc, so I will attempt to answer your questions for you.
The moon appears to be a nearly perfect counterpart to the sun. They appear to be about the same size as one another and about the same distance from the earth.There is no similarity between the sun and moon at all apart from their apparent size in the sky and the fact that they both appear to be round. The sun is much further away, but appears a similar size because of it's vast distance from us compared to the moon. The Sun is about 92 million miles and the moon about 240,000 miles. The moon's diameter is about 2000 miles and the sun's is 400 times larger, but as the sun is also 400 times further away they look the same size from the earth.
If the sun is a big ball of fire, than perhaps the moon is a big ball of ice.If the moon were ice, then spectral analysis would show it, but it is just a ball of rock and dust basically.
Does the moon emit its own light?The moon reflects the light from the sun, which is why there is an eclipse when the sun, earth and moon line up and the earth blocks the light from the sun. You can also see that the moon doesn't emit it's own light when the sun is to one side of it so you only see part of the moon reflecting the sun's light.
Does lunar light cool as sunlight warms?As the light from the moon is purely reflected it doesn't directly radiate heat, however the surface of the moon that is in sunlight will warm up.
The moon has a face just as earth is said to have a face when viewing it from space.When we refer to the face of the moon or earth, we are not comparing it to a human face, but the side or 'Face' that we see, rather like 'the face of a cliff'. Sometimes the moon appears to have two eyes and a mouth during a full moon, but that is just the positioning of surface features.
The moon has two primary colors, dark grey and white.Basically correct, although the white is more a lighter grey.
Perhaps the dark grey color represents liquid and one material and the white color a solid and another material, or vice versa.It has been known for centuries since the first telescopes that there is no visible liquid on the surface, although the darker areas are known as Mare or Seas as some of the early observers thought they could be seas and named them as such. We still use the same names now and if you look at the moon through binoculars or telescope you can clearly see the darker areas and the craters on the moon caused by meteorite impacts.
Sometimes the moon changes color, occasionally it's red, blue or golden. I wonder what these color changes represent? The moon itself doesn't change colour, it is the effects of us viewing it through the earth's atmosphere that makes it look different colours sometimes. So a reddish dust cloud in our atmosphere could make the moon appear red, but there are many other conditions that can produce different apparent changes but are mainly changes in our atmosphere.
Maybe the lunar weather is changing, or vegetation on the moon periodically goes through metamorphosis.There is no weather on the moon as it has no atmosphere, for the same reason there is no vegetation.
I hope some of that helps you and I should add that my answers come from a round earthers perspective although I am quite sure that some but not all of them will be agreed with by flat earthers.
Roger