Yes, there are test kits for Nitrate, Phosphate, and as you already know, you can determine the CO2 concentration with a pH/KH reading. You will not be able to find your Potassium level, but dosing KNO3 (Spectracide Stump Remover - found at Walmart) will add Potassium and Nitrate.
If you test your tank water and find no Nitrate present, then add about 1/8 to 1/4 tsp of the stump remover and test again in about 15 minutes (so it mixes thoroughly). You should get it somewhere around 10 to 15ppm (although up to 20ppm isn't a problem). Buy a cheap, but more importantly, easy to use Nitrate test kit, because you will be testing frequently until you set up a fert schedule, and even then pretty regularly. Buy Fleet Enema (or a generic brand, like I use) and add maybe 2 drops after your water change. Keep this level around 1-2ppm Phosphate, but no higher. Sometimes it's hard to find a Phosphate test kit, so I order my kits online. I use Seachem Phosphate test kits, personally. With that high of light output you may run into other algae issues without a more consistent CO2 output. I'd suggest using Flourish Excel along with your DIY CO2 just to make sure there's enough available. For your small tank, it's pretty economical.