Live rock can't leach nitrate. Phosphate can adsorb onto the rock, but nitrate can't. The nitrate could be coming from dying animals in the rock, or perhaps some organism is fixing nitrogen from the air. In most cases, nitrate originates with the food.
I agree that the flow should be fine. Have you tested the RO-DI output? There might be a test kit issue.
I wouldn't remove live rock from the tank to scrub it, if that's what you're doing. That could kill organisms and feed the algal bloom.
I'll have to think a bit about this one.