If you are using a API master kit to test your nitrate, you have to be careful on how to proceed. It has been a long time since I used it, but from what I remember the solution bottle requires you to shake it for a minute or so before even using it. Then after the mixture, once again you have to shake it. Otherwise the result will be 0ppm for nitrate. I have made the mistake at one point when I forgot to shake it.
Yeah, ammonia and nitrite are both toxic. Fish can't live long even where this a trace amount of either in the water.
A fully planted aquarium of minimal 20-gallon with every square inch covered with plants might support a single Neon Tetra sized fish without a filter. You can't count on the plants to absorb all of the ammonia produced by the fish and the leftover fish food.
I wouldn't worry about phosphate. All the things you are adding to your aquarium will eventually result in an algae boom. Once your fish tank is fully stocked, combined with eco-complete substrate, there is very little else your plants need.
I have had very little experience with CO2. I have used a reactor type of system years ago. It produced CO2 upon chemical reaction at a slow pace. Once your CO2 is fully operational, please share your experience as well.