Afaik fertilizer enriched aquatic planting soil has the macro nutrients covered, but trace elements will probably need to be added, you can buy the super master test kits which have iron test in them. The planting medium isnt just for nutrient supply but also a better substrate for the roots to dig through and hold on in. I'm growing DHG right in the sand and the only issue I have had with it is it was getting uprooted easily for the first week or two until the DHGs roots made it down to the gravel substrate under the sand. Planting medium should help with that and give you a bonus of nutrients.
As for the light my tank has a single t8 6700k bulb and approximately 2ft of water above the grass, it grows and carpets, but very slowly, you might want to upgrade to a 18000k bulb and/or a dual bulb setup for faster growth and spread.
Co2 is the other half of photosynthesis I strongly recommend a pressurized kit to provide co2 for the plants.
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