Using only fish waste and Phosphates for dosing aquariums is a common form for El Natural type highly stocked aquariums. How do they get away without dosing anything? Simply, fish waste (ammonia) get's turned into Nitrate via the Nitrogen cycle.
The basics of the Nitrogen cycle in regards to aquariums: Fish Waste (Ammonia) --> converted by nitrifying bacteria to (Nitrite) --> (Nitrate).
Phosphates are introduced via fish foods.
I define an established aquarium as an aquarium that has a substrate and/or filter that is enriched with at least 3 months of fish waste, detrius and the nitrifying bacteria. Colonies of bacteria are the most important component that defines "established". The combination of all these aspects ensures that waste is broken down into nitrates for plant utility.
By removing fish from an establish aquarium, one removes the food source (waste) for the bacteria. This thereby, reduces the amount of bacteria in the tank and because of this, nitrate levels would likely decrease unless additional ferts are added.
EI is estimative, the additional dosing of all Macros and Micros in tandum with fish waste & food won't hurt anything as you have already seen. However to answer your question, if you have a high fish load, you probably could get away without dosing N & P, and instead rely on the waste, established substrate, and fish food as your main sources of these compounds.
I hope that was somewhat helpful, you had a rapid fire set of questions. My answers/suggestions could easily be expanded several paragraphs more. But I think you get the gist.
-John N.