Just so you know, there are some in the saltwater field that would die for a 20ppm nitrate reading. Your diatoms are a normal part of a new tank and use silica (often found in tapwater and common non-argonite sand ; play sand/pool sand/etc) They'll die out on their own. What kind of sand did you use? Tap or Ro
regarding the algae, the nitrates don't help however the other contributing factors would be a) any direct/indirect sunlight hitting the tank? How long do you have the lights on? How old are the lamps?
FWIW: a lot of us go through algae spurts in the summer months due to the intensity of the sun changing, the direction of the sun and the duration of the day changing. With the increase in the ambient temperature of municipal water sources the water company will begin to adjust the treatment process to keep the water supply within acceptable parameters. This could mean adding things that adversely affect your tank (assuming you use tapwater).