OK. The Nicrew will be fine for your low-tech tank (low-tech meaning low-medium light and no CO2 injected). Depending upon your fauna load you may need a filter, but you can try without one and see if your plants can handle the organics, so long as you keep up with the water changes and watch the ammonia. If I were you, I would get Seachem's "Ammonia Alert." It is placed on the inside of the tank and will allow you to see ammonia levels with a quick glance. You can remove it once you're confident you have a stable, ammonia-free, environment. Filters can do a lot in terms of keeping the organics down and trapping debris. So, keep in mind that even a small one could do a lot for you.
Sounds like the substrate is inert, so all of your fertilizer can come from the water column. When you get your test kits, test your tap waters' GH. In the meantime, check this forum for the ideal GH and pH conditions for your shrimp. You may need to use something like "Salty Shrimp" depending upon what you find your GH to be.
For the plants, they will need the three macros: N (nitrogen), P (phosphorus) and K (potassium). The Leaf Zone only supplies K and iron. In a low-tech setup, fish waste will usually supply enough N and P, but I don't know how many shrimp are needed to do that job. So you will probably need to add N and P. Additionally, plants need trace minerals. If it were me, I'd get rid of the Leaf Zone and buy something like NilocG's "Thrive S" to feed your plants everything they will need.