The fuzz on the fake plant leaves is brush algae. The different angle of the photo showing the rock is a bit hard to see (for me anyway) but we can assume it is the same algae.
So, back to your initial question, you cannot really get rid of this as it is going to appear so long as you have nutrients (from the fish, from ther source water) and light. However, increasing your water change volume to half the tank will help, but not to the extent you may prefer. Reducing the light period can also help. You don't have live plants to fuss over with light, so you could have the tank light on a timer and only have it on when you are normally around to view the fish.
On the light, a timer so this is consistent is best for the fish. Fish, like all animals, have a circadian rhythm that is governed by light. We humans mainly perceive light with our eyes, though to some degree our cells pick it up too; in fish this is much higher, through their cells and their eyes. And like us, their internal physiological processes are managed by this light. So it is important not to be turning the tank light on and off, but maintain a consistent period of light and dark every 24 hours. And because fish do not have eyelids to adjust the light, It takes about half an hour or slightly longer for fish to adjust each time the light comes on or goes off, so the more this occurs, the more stress will be inflicted on the fish.
Any idea what the nitrates are? I would expect them to be high, by which I mean higher than say 20 ppm. I will assume the GH is high (for the African rift lake fish) and the pH too. The harder water ironically helps algae, but here you can't do anything about that.
Byron.
