So it actually is as simple as mathematical addition and subtraction.
You add fish food, it has in it nitrogen compounds that your fish turn into ammonia for your bacteria to turn into nitrite and nitrate, as you know.
your plants consume that nitrogen, depending on the plant, how densely planted, light saturation, etc etc, but essentially when they grow, they are removing Nitrogen from your water.
In order for the sum of this math problem to be zero, the nitrogen production needs to equal the nitrogen consumption. The way you can verify it is, as has been stated, testing for nitrogen. All this said, you absolutely can and should let plants live all over your tank, they will reduce your maintenance burden, look beautiful, and make your fish feel more at home.
The top off question, once again, others have touched on it, but every time you add tap water you aren’t simply adding H2O. All the minerals and chlorine are also along for the ride. If you have livebearers or rainbows or African cichlids that love insanely hard water, you may get away with the minerals part, but nothing alive likes chlorine. You have to at least let it evaporate out of the tap water. ACO’s test strips are awesome for this because they include a chlorine test pad. Pour a 5 gallon bucket of tap water and check it. Then let it sit out for 24-48 hours and test it again. (Then do it with an air stone in there to see what it does)
TL,DR: Topping off works best if you use RODI, have a massive plant to fish ratio, and test for Nitrogen regularly. But it can work.