Personally I don't worry myself with pH, kH, and gH. They are difficult to change long term and seem rather useless to me unless you are keeping some sort of plant or creature that absolutely demands certain numbers. What comes out of your tap is what comes out of your tap. The fish will have to deal with it. In my opinion the stability of these things is more important than their actual value...as long as that value is within reason. Your tap pH is fantastic, but here is some explaination.
Per Hydrogen (pH)
The pH of the water is a measure of the balance between the Hydrogen (H+) and Hydroxide (OH) ions in the water. I think most of us know that low pH is acidic and high pH is alkaline or basic. Hence a pH of 5 is slightly acidic water, a pH of 7 is neutral and a pH of 8 is alkaline water.
Carbonate Hardness (KH)
This is an area where many people get confused. One of the reasons the term alkaline is avoided a bit and the term Basic is used for the pH scale is because this reading is measuring the alkalinity of the water. It is not the same as alkaline.
The alkalinity is a measurement of the waters buffering ability, or its ability to absorb and neutralise acid. Clearly the more alkalinity or the higher the Carbonate Hardness of the water the less likely you will incur pH swings in the water.
General Hardness (GH)
This is essentially a measurement of Magnesium and Calcium ions in the water. Again it is measured in the German degrees of hardness scale or parts per million. This is what is generally meant by soft and hard water which are terms people should be familiar with. The table below shows comparisons between parts per million, the dH scale and the generalised concepts of soft and hard water.
The rest of the things you posted are important. Ammonia, Nitri
te, and Nitra
te are the pollutants/elements in what we commonly call the nitrogen cycle.
I'm going to break it down simple, then link you to a proper explanation.
Fish poo, fish food, and stuff create ammonia. Ammonia is bad and very toxic to critters. After a while (days-weeks) bacteria show up, magically, that like to eat ammonia. This is good, but those bacteria make waste, nitri
te is bad and very toxic to critters, just like ammonia. After the tank has a presence of nitri
te (days-weeks) another type of bacteria show up, magically, that like to eat nitri
te. This is good. This second type of bacteria also create waste, nitra
te isn't the greatest stuff on the planet, but it isn't nearly as toxic as ammonia and nitri
te. You critters can handle a relatively high amount of this. Water changes take care of the rest.
The good news, plants, to an extent, do work on all of the above. This is why planted aquariums are better for fish.
The bad news, having plants, without fish...means you probably haven't started the above cycle to any great extent. This is why you hear people talking about "fishless cycles" all the time...to get this cycle rolling. Bacteria are very supply and demand creatures. If there is nothing to eat...they go way...if there is lots to eat, you get a lot more of them. Adding too many fish too fast can overwhelm the system...sort of a supply and demand slinky affect. To get this started you can add a few fish, and do lot's of water changes until things get rolling. You can add fish food (without fish) and get things moving. Alternatively you can actually add ammonia to get things kicked off.
It normally tanks a few weeks...but your tests will go like so...give or take.
Week 1: Ammonia 5, Nitrite 0, Nitrate 0
Week 2: Ammonia 2.5, Nitrite 2, Nitrate 0
Week 3: Ammonia 0, Nitrite 3, Nitrate 2
Week 4: Ammonia 0, Nitrite 0, Nitrate 4
Now I just made these numbers up as an example, but hopefully you can see the pattern. This cycle may take a week, might take a month...lots of variables and lots of different things can effect it. It looks like from your results you may already have this cycle going. I would add some fish food and see what happens over the next week. You tank is ready to go when everything is 0 except Nitra
Check out this link for a more scientific approach lol.