Nitrate does not have to be at 0. Anything 20 or less is absolutely fine. Nitrate is the byproduct produced by cycling and it's fine.

You shouldn't have rinsed the filter. The good guy bacteria live in the filter and you may set your tank up for a mini-cycle.

Your tank doesn't need meds at the moment. Ammonia readings are caused from overstocking the tank.

Please read all of the links we posted above to the two goldfish sheets and the article about cycling.