The sun shines light on the moon and the moon reflects it to us. So, if the moon didn't "shine" light, the sun wouldn't be shining light, so, no, we wouldn't be able to see the moon or anything else in the world.
By 'not bright' I'm assuming you mean black, or dark in color. And yes it would still be visible from earth if it was a darker stone color (or a darker colored dust). To be completely invisible it would have to consist of an almost completely flat black color.
The moon reflect of the sun. The different moon phases are because of different angles the sun is hitting it. The moon is at some point "not bright" during a new moon. You can't see it then so, yes, you will not see it.