Thanks Maverick, and your plants look great, you raise good questions, and I am not a scientist. But I am a keen gardener and I have kept tropical fish from my childhood and have successfully maintained planted tanks for some four decades, sometimes with rather more algae than is ideal.
Some garden plants need soil with a lot of richness, (in farming Corn needs a lot of fertiliser to produce good yields) and well rotted manure works a treat, as does bone, hoof and blood, or/and chemical fertilisers. Some plants even benefit from foliar feedings in the growing season. Roses love a good feed, Californian poppies really don't. Try a wild flower mix on Nitrate rich soil and things don't go well, most wild flowers need low nutrient soil, but some species of grass, love a rich soil and with other 'weeds' dominate a rich environment. Some folks have to remove a few inches of top soil to have success with wild flowers. Their garden soil is simply too rich, the same applies to arable farmland, it can take years to get the Nitrate levels down to successfully grow a wildflower meadow. Nitrate levels in the water in unpolluted rivers can be really low, way lower than we can measure with our hobby test kits.
Most aquatic plants come from low nutrient waters, very low in fact, less than 1 ppm Nitrate, but many plants have their roots in rich humus packed substrates. It never ceases to surprise me how greedy Crypts and Amazon swords are, plant them in a really rich substrate, or add loads of nutrient capsules and they grow lots of leaves. Many plants in rich water suffer badly because algae grow quickly and cover their leaves.
Inject CO2 and use lots of light, and many plants get very hungry, whether in a fish tank or in a greenhouse.
Here in England you never need to feed any outside garden plant October to March, but in June or July when the day is long and temperatures are higher, some plants need fed heavily, tomato plants can be incredibly hungry, and they benefit from a Potassium rich feed, which is why I sometimes, but not often, add Tomato feed to my tanks, but since tomato feed contains a fair amount of Nitrate and Phosphate I can easily overly enrich the water column and get a green algae outbreak.
Floating plants with access to the high levels of atmospheric CO2, and perhaps more importantly, inexhaustible, levels of CO2 in the atmosphere, if light and temperature is also good, can fairly quickly deplete the water column of Nitrate and Phosphate and show deficiency signs, the so-called Duckweed Index.
With medium light and a rich substrate and either no CO2 injection or modest injection (water column <10 ppm of CO2, but >5 ppm) I would guess with normal fish stocking, the faecal matter and left over fish food would ensure more than enough macro nutrients were available. However, in hard water I have always, however, had to add chelated Iron.
The Father Fish method, works, to a point, no water column fertilisation and little by way of water changes - though his tanks are never that impressive to me - I suspect, they work because the substrate is very rich and he uses a lot of light, a lot, I asked him, four 100 watt floods on one fairly shallow tank, and easy plants.
I have always found Walstad tanks hard to get through the first 6 months but after that they work pretty well, with moderately soft water, easy plants, modest lighting, humus rich soil and CO2 from, as some others have suggested, decomposing wood (cellulose etc.) releasing modest amounts of CO2.
In the British Isles house plants do not ordinarily need to be fed during the winter, come spring and extra light, and they benefit from a feed, by the summer they need a feed, sometimes weekly. If plants are in a commercial greenhouse and are being illuminated with powerful Red & Green lighting in addition to the sunlight, and kept warm, they need regular feeding. Aquatic plants in an aquarium are not however, comparable to hydroponically grown plants, the latter only have their roots in the water and the nutrients, aquarium plants have their leaves in the water, high Nitrate and Phosphate levels will produce conditions for eutrophication, and the plant leaves get smothered by fast growing algae. High Phosphate and high Nitrate levels in the summer in the UK often produce algae blooms which sometimes literally poison animals and choke plants and aquatic life, the BOD issue.
As I have said, I am not a scientist, I will be interested to read any observations on my responses.