What would happen if we painted the whole moon with black, will it still reflect light, or it will become invisible?
What would happen if we painted the whole moon with silver paint or make its surface shiny?
The moon is already a pretty dark grey. It only reflects about 12% of the light that hits it. It is about the colour of (worn) tarmac on the road. You can see how grey it is in NASA's gif from a million miles away.
"Black" paint reflects less light. Common household black paint reflects only about 5% of light. So the moon would be rather less than half as bright as it is now. But you could still see it. There are some specialised black substances that reflect as little as 0.035%. A moon coated in these would actually be hard to see.
White paint and silver paint reflect about 80% of light, so if the moon were white it would be about 7 times brighter, but much less bright than the sun which is about 400000 times brighter than the full moon.
The albedo of the Moon (the proportion of the light that falls on it which is reflected) is about 0.12. The darkest known material is Vantablack with an albedo of about 0.0004. So if you painted the Moon with that, the reflected light level would drop by a factor of roughly 300, taking the magnitude of a full moon from -13 to -6 or so. This is still brighter than the Moon appears when illuminated by Earthshine during a lunar eclipse (about -3), when it is still perfectly visible, so the Moon would not become invisible.
In the other direction, making the Moon perfectly white would increase its brightness 8 fold or about 2 magnitudes, taking it down to -15. This would make moonlight a bit brighter, but probably not change anything fundamental.