I'll do a brief explanation to cover both aspects.
Aquatic plants require light of sufficient intensity (and spectrum) to drive photosynthesis. The faster growing plants need more intense lighting than slow growers. Duration does not compensate for inadequate or excessive (too much) intensity.
Light must be balanced with nutrients. Without nutrients, regardless of the light, plants cannot grow. Aquatic plants require 17 nutrients; some are macro-nutrients and some micro-nutrients. The level of nutrients must be in balance with the lighting; if not, algae usually takes advantage and either this or the lack of nutrients will kill the plants. The plants that are faster growing need more nutrients in balance with the light than do slow-growers.
Floating plants (Water Sprite, Frogbit) are fast-growers. This is because they get stronger lighting being at the surface. They also have what is termed the aerial advantage, which primarily involves CO2. Carbon is one of the macro-nutrients, and often the first to "run out" in an aquarium. The aerial advantage involves the floating plants' ability to assimilate CO2 from the air as opposed to from the water as occurs with fully submersed plants; for the floating plants, air CO2 can be taken up about four times faster than assimilating CO2 from the water.
That's the carbon dealt with; you will never need to dose carbon with floating plants. The other 16 nutrients may occur within the water, but levels may not be adequate to balance the light. Nutrients can be added by using fertilizers. With fish in the tank the feeding of the fish, plus water changes, replenish some nutrients but it depends upon the fish load just how sufficient these may be.
You want a complete or comprehensive fertilizer. Taking the Seachem Flourish Comprehensive Supplement for the Planted Aquarium since you mention this product, it contains all but three required nutrients. The three missing are carbon (covered above), oxygen and hydrogen; the latter two are obviously always present in water so they can be ignored. Of the remaining 14, all are in FCS but some of the macros (namely calcium, magnesium, nitrogen) are minimal because the manufacturer assumes most water supplies have sufficient calcium and magnesium, and nitrogen is taken up by plants in the form of ammonium (ammonia), which normally is in plenty of supply from fish respiration and decomposition of organics. If there are no fish in this plant tank, nitrogen needs to be added as the ammonia/ammonium will probably be insufficient.
The other nutrients in FCS are in balance according to the requirements of the plants. This product, as the name indicates, is a supplement to nutrients already present, as I described above. The low nitrogen will likely be the limiting factor; I see this in my QT tank for new fish which has floating plants but no fish; the plants are clearly surviving but not thriving, and ammonium is the issue.