Can proof coins turn black? And can the mirror like look fade over time?
If they are exposed to the right elements, they can tone like any other coin.
The mirror is due to the polished surface. That can't "fade" on its own.
If the proof coin is mishandled it can pick up scratches or "hairlines" that will reduce the smoothness/mirror.
The mirror effect can also be reduced by significant surface oxidation or reaction to outside elements.
And, yes, a proof coin could turn black under the "right" (bad) conditions if it tones or tarnishes heavily enough.
Search for photos of old proof coins (there are plenty that get posted on the forum). If proof coins are properly cared for, if/when they tone it is far likelier to be a pleasant color.