If the GH and KH are in ppm, then your water is very soft and hasn't got many minerals in. Soft water is good for tetras, Corydoras, rasboras, angelfish and South American dwarf cichlids, but it is bad for livebearers like mollies, platies, swordtails & guppies.
Most barbs & danios are fine in soft water but do better in water with a GH around 150ppm. They should be fine in your water tho.
Basically avoid mollies and other livebearers and the rest of the fish you listed in Post # 3 should be fine.
------------------------
You don't actually have an ammonia test kit and they are helpful when first setting up a tank. You can buy the kit separately and the liquid test kits are usually a little more accurate. When buying test kits or medications, check the expiry dates and don't buy any that are kept in a warm room. Heat destroys the chemicals in them so try to avoid buying them if they are next to a window or something that produces heat (like a fridge). And don't buy them if they are in a fish room.
Keep your test kits in a cool dry place, out of reach of children and animals, and wash your hands with soapy water after using them.
------
Ammonia and nitrite should be tested several times a week during the first few months of a tank's life, then you check them if the water goes cloudy or the fish look unwell or die.
Nitrates can be checked once a week after the filters have cycled. Nitrate test kits will read nitrite as nitrate, so if there is nitrite in the water, you get an inaccurate reading.
GH and KH can be checked once a month if you like, just to make sure the water company hasn't started altering the water. they don't normally but it's good to check every now and then, just in case.