While it is true that some plants can manage on the natural nutrients from feeding fish, it depends upon the plants and the fish load. But even so, all the necessary nutrients (there are 17) may not be available, and this will affect plant growth. Faster growing plants (all floating plants are fast growers) naturally will need more nutrients than slower-growers like Java Fern, mosses, Anubias, etc. There is no harm to fish using a comprehensive supplement provided it is not overdosed. There is also substrate fertilizers like Seachem's Flourish Tabs. These are remarkably good for substrate-rooted plants like swords. And the nutrients do not leech into the water column, but remain in the substrate where plant roots assimilate them. No benefit for floating plants like Salvinia obviously.
To the brown, the light intensity can cause this, but also a lack of certain nutrients. I would try a comprehensive supplement such s Seachem's Flourish Comprehensive Supplement for the Planted Aquarium, or another near-identical product is Brightwell Aquatics' FlorinMulti. If you are in the UK, there is TNC Light.