A photo not so close might be better, but the "fuzz" on the plant leaves is black brush algae. Probably the same is on the tank glass.
It is not harmful to fish directly, but it may indicate problems with the water quality, depending. Algae is natural in any aquarium; it needs light and nutrients. If you have live plants, you need to keep the light and nutrients in balance sufficient for the plants so algae will not have the advantage. Light intensity and duration both factor in; nutrients come from fish load, fish food, and plant additives if any.
Byron.