Plants need about a dozen or more elements to grow. When any of them are lacking the plants will not do well, and may die. When some are present in very low amounts the plants sort of survive, but various types of algae can grow.
By supplying all the fertilizers and minerals that the plants need they will grow well, and keep the algae and Cyanobacteria away.
IME aquarium plants use more potassium than other nutrients, and the other one I needed to dose early on was iron.
If the plants in your tank are keeping the NO3 at the bottom of the test chart (<5 ppm) then I would sure dose nitrogen. Ammonia and nitrites are supposed to be at 0 ppm, but some tests might show a blush of color that means nothing if the tank is well cycled and stable.
I would dose phosphorus, too. It does not take much, but that little bit is required.
Absolutely yes potassium, and iron.
Trace minerals are important, too. If that is the one that you are just calling Flourish, or if it is Flourish Comprehensive, then go for it!
Excel is indeed a way of getting carbon to the plants. If you are already OK for CO2, then no need for Excel.
If you have only the one small tank, then the Seachem liquids will last you a long time. However they are not really an economical way to buy fertilizers. You are buying water with a teaspoon or two of the minerals the plants need. Buy them once, practice with your tank and see what you need, and how much. Then you might want to look into dry fertilizers, where none of the purchase price is buying water.
is one source.