There are dozens of different species seen under the common piranha label; presumably the species here is Pygocentgrus natgtereri. I have never kept piranha but I do know they need much larger quarters, so I will agree with mikey and move to the algae issue.
This fish produces a lot of waste, and that is undoubtedly one issue, as this becomes nutrient for algae. I would increase the volume of water changes to at least 60-65% of the tank volume, once a week, though more often might be advisable to get this algae under some control. Dig well into the substrate during water changes to remove as much organics as possible. Obviously, remove as much of the algae especially from the glass and substrate as you can the first W/C.
I am not familiar with UV filters alone, but I would suspect this may not be adequate; ordinary filters such as canister would certainly clog with organics within a few weeks, and these must be kept clean to help. One thing I can say is that UV will not prevent/kill any algae that attaches to surfaces. Unicellular algae such as what causes green water can be killed by UV but only if all the water travels through the UV before any of it returns to the tank.
Nitrates at 20 ppm...have you tested the source water for nitrate? If the 20 ppm is occurring solely from within the aquarium (meaning, nitrate is zero in the source water) this is high which one would expect here. Getting the organics/nutrients under control will lower nitrates, certainly below 10 ppm and down to between 0 and five would be advisable.
The light I can't comment on, but as it is only on for 6 hours I would suspect the organics/nutrients is the main culprit. The higher plants simply cannot utilize all this, hence the algae takes advantage as it is no where near as fussy over such things.
The plant fertilizer...which product and how much? This is a well known cause of algae issues when it is adding nutrients that are not needed by the plants, as here. I had serious brush algae solely from liquid plant fertilizer dosed twice a week; down to once it disappeared, and I tried this twice to confirm. In your situation, even once is probably way too much, given the natural-occurring organics. I would consider stopping this, subject to finding out just what it is. One thing that does help in this sort of situation is to use only substrate tabs and no liquid. I got around algae issues doing this too. Seachem's Flourish Tabs are complete substrate nutrients and ideal with swords and larger substrate-rooted plants. The nutrients do not get into the water column like they do with liquid additives, so that helps avoid algae.
