You have asked a big question. In a nutshell, most aquarium plants will manage in whatever water you have. It is the fish that have preferences that cannot be overlooked.
An aquarist should always start with what comes out of the tap (the source water). If this can be used, it will make water changes easier. Adjusting the water chemistry is not always easy, and if not done properly can be dangerous to the fish. More momentarily.
You specifically asked about levels of GH, KH, CO2, NO3, K+, PO4, Fe, & Ca.
I never bother with the last four (Potassium, Phosphate, Iron and Calcium), by which I mean I never test for them. Calcium, and perhaps potassium occurs in most municipal water. Calcium is the prime mineral for hardness (GH). Unless like me you have very soft source water, adding calcium will not normally be necessary. Potassium might need to be, but this is contained in the good comprehensive liquid fertilizers and substrate fertilizers and except in rare situations it will not be necessary to specifically target potassium. Phosphates are introduced via all fish foods, and provided there is a decent number of fish being fed daily, the phosphate will usually be more than sufficient. Iron may occur in tap water, and it is included in all comprehensive fertilizers and usually at sufficient levels.
NO3 (nitrate) I rarely test, since my established tanks are fairly heavily planted and thus the nitrate is very low and stable. It runs < 5 ppm. The lower the better for fish, and aquatic plants do not need nitrate. Nitrate should never be added to a natural planted tank [although it is minimally present in some fertilizers but this is not an issue]; removing it is more important if it occurs for instance in the source water. Nitrate has more of an impact on fish than many realize, even at moderate levels.
CO2 I also never measure. This occurs naturally in all aquaria with fish. Fish and plant respiration creates CO2 continually, and even more occurs from bacteria breaking down organics in the substrate. If you intend a natural (low-tech) planted tank, there will be sufficient CO2 naturally, although one has to be careful to have the light balanced, then the other nutrients. As soon as you start adding diffused CO2, you are raising the level of balance significantly, and light will have to be more intense and other nutrients will almost certainly have to be added more often.
That leaves GH and KH. The tap water (source water) values should be ascertained before the tank is even set up, and now I come back to my earlier comment on adjusting water chemistry. Some fish need medium hard or harder water, some do not; some are adaptable within limits. Working with what comes out of the tap is easier. But there are safe ways to alter the water chemistry if this is needed.
Now to your fish and pH/hardness. You have a mix of soft water and hard water fish, and a pH around 7.2 will serve all of them generally. We need to know the GH and KH of the tap water though. The livebearers (molly in particular, but
Platy too) need minerals and this means medium hard or harder water. The tetra in particular and also the gourami and angelfish need softer water, though these can somewhat manage in medium hard. When I have the GH and KH numbers I may have more to suggest.
Byron.
and in doing so here I see I neglected to comment on some plants that do have some preference to water chemistry, here GH again. Vallisneria is one that really is much better in medium hard to very hard water; it actually grows naturally in the rift lakes, Lake Malawi I think, or maybe Tanganyika, or both...whatever; it struggles in soft water. Mosses on the other hand can have difficulty in hard water unless there is plenty of CO2. Most plants will be OK except perhaps in extremes, too hard or too soft [I have the latter problem and have to add calcium, magnesium and potassium].
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