Well it doesn't do any good for ammonia to be at 0 if there was never any ammonia present
However, the fact you're seeing nitrates means your tank should be cycling. Now it's a matter of waiting for nitrates to go down (though 10-20ppm isn't high, I like them to drop down to 5 before I add livestock, just personal preference).
As far as FSS, not sure if it will support HC but it shouldn't be moving at all when you add water in. Disturbing the substrate is not good as it can release tons of bacteria in the water column...might be non issue now but in a few months with livestock in there could be a big issue. I pour water onto my hand into the tank (hands cleaned thoroughly and dried before I do this). I put my hand right where the back of it touches the top of the water in the tank, then pour the new water into the palm of my hand and let it fan out into the tank. Breaking the flow like that and giving it a surface to spill over keeps your substrate from being disturbed. You could use something like a plate or bowl and hold that if you don't want to use your hand I suppose.