Diatoms in new tank setups are very common. The generally go away on their own once excess silicates in the water are used up. Lighting does indeed contribute to the problem and anytime there is an algae issue lights should only be left on 6 hours daily.
One thing I noticed you said tho is that you have nitrite, very high at that. Was this a mis print? If your tank is months old (knowing exactly how old would be helpful) and your having nitrites then your tank isn't cycled. And you need to do some 50% WC's to get nitrite levels down to .25 or below for the safety of your fishes health.