One good floating plant not yet mentioned is Water Sprite, Ceratopteris cornuta. This species is the true floater, and it does better floating than planted; there are two other species that are better planted. Like water lettuce (Pistia stratiotes) and Frogbit (the true tropical species, Limnobium laeviatum), once settled it can get large, but the many daughter plants produced on alternate leaves can be gently pulled off and kept with the main plant discarded if you want to keep the surface more open. Ceratopteris can cover the entire surface of a 48 by 18 inch aquarium with just one plant when conditions are to its liking.
To your question of nitrates, live plants will help keep these down, and floating are the best for this because they use more nutrients and grow very fast. But there is a limit to this assimilation of nitrate; aquatic plants prefer ammonium over nitrate, so they take up the ammonia/ammonium faster than bacteria, and the nitrates are thus less because the ammonia/ammonium has been primarily used by plants which do not produce nitrite and then nitrate. However, there is likely also uptake of some nitrate as well, more by some species than others. But this is not great, so if there is a serious nitrate problem, such as high nitrates in the tap or well water, these are not likely to reduce all that much because of the plants, but everything is relative.
Byron.