How long are your lights typically on for? Does the tank get any direct sunlight?
Likely cause is too much light. Lights should only be on for 6 to 8 hours per day and the tank shouldn't get direct sunlight.
Turning off the lights for a couple of days wont change anything. You either need to reduce the lighting period over a much longer period of time or, assuming you dont have live plants, a complete blackout of the tank for a week or so. If you go the blackout route no light whatsoever, cover with a dark blanket, lift the blanket in the dark to feed.
If your tests are all zero, there is possibly something wrong with your tests or you are testing after near 100% water changes. If you are cycled you should see nitrate, if you arent cycled you should see ammonia and/ or nitrite depending on how far really along your cycle has progressed. Make sure you are doing the tests properly, as per previous thread really give bottle #2 of the nitrate test a good shake, bang it on a counter top. If that still doesnt show anything get a 2nd opinion.
It could be the duckweed is consuming all the nitrate however, so if testing really shows everything is zero i wouldnt worry too much. I would however get an all in one liquid fertiliser that has a good amount of nitrogen as the plants wont be getting enough of this essential nutrients from the water. Something like NA
Thrive if its available in your country of origin.
Your platys will eat a little algae if they are hungry. Mystery snails arent as good algae eaters as nerite snails, and a cory will have a go at it if they are starving. You dont really have any known algae clean up in the tank. And nothing will eat the algae causing the green water.