Mold stains. The stains remain long after the mold is dead. It looks to me like mold stains that were bleached, which will kill the mold. Bathroom paints often have anti-mold chemicals in them. If you are worried about the appearance, you can paint, but I would not worry about an active case of black mold.

Some day I will open and online lab that does testing analysis via pictures at half price of brick and mortar joints charge for samples. Think I'll get any takers?

It looks like your fan is not the proper cfm and water is dripping down the walls when someone showers. We had that in one of our bathrooms and installed a more powerful fan.

Bleach doesn't necessarily kill mold- on porous surfaces it doesn't get to the roots and just makes the surface bit turn white. OTOH, vinegar does kill mold.