One thing has me worried about possible measurement error in your readings. You show two readings the first of which has GH at 300 ppm then at 75 ppm. Something there is wrong. Turn 300 into 75 would require a massive water change using RO/DI (pure) water. I would say it would take a 75% change at least.
When it comes to chemistry, water can be strange stuff. For many fish keepers things work out without much thought or effort. For the new fish keeper, this is as much luck as anything else. Things behave differently when dissolved in water than they do elsewhere. This creates the potential for two areas where one might have problems. The fiirst is cycling and then next is in the choice of fish.
The second problem happens when one tries altering ones tank water parameters from their normal tap levels. It is an almost impossible challenge for new fish keepers. The exception might be if you are familiar with chemistry. So, the first thing I am going to suggest is that you get some input on the basic chemistry most fish keepers should know. To that end please go here
http://fins.actwin.com/aquariafaq.html then click on
Your First Aquarium. I suggest you read through most of it twice. But please pay particular attention to the sections on Water Chemistry, It is pretty basic and written in an easy to understand manner. it will give you some grounding in what is going on in your tank.
I have only been in the hobby for 20 years and I have had 20 or so tanks for most of the last 15 of them. It took me about 14 of those years before I was willing to attempt altering the parameters in one tank to keep some difficult fish. It took me some time to get it right and a few dead fish. I have a $250 continuous monitor on the tank now which tells me TDS/Temp/pH.
One of the best pieces of advice frequently given to new fish keepers is to chose fish which will normally thrive in one's specific tank parameters. In your case this would appear to be more towards African rift lake cichlids than S. American fish. This would eliminate problem #2 above.
As for your water parameters. You do not list ammonia. In your water parameters ammonia is pretty toxic even at low levels. Basically, ammonia gets more toxic the higher the pH and temperature. Nitrite is best handled by adding small amounts of salt to one's water, This will prevent more nitrite from entering the fish. It also allows the nitrite that is already doing harm inside the fish to be removed. Nitrate levels should be kept below 20 ppm longer term.
One thing appears clear, your tank is not cycled and that is what harmed the inhabitants. Doing a fish-in cycle in your water parameters is pretty tricky because the ammonia gets dangerous fast.
An observation about fish, water changes and stress- one of the major things that facilitates health related issues in fish is stress. The more they are under, the less effective their immune system is. When we set up a new tank and put in new fish, consider things from the point of view of the fish. it has been caught an bagged several times in the recent past, it has likely been moved to different parameters a time or two along the way and it is almost certainly underfed. So it is in a strange environment which in unhealthful due to cycling issues. Now we poke a hose into the tank, likely move it around some and we drop water levels fast. This is simply more stress. It also has the effect of slowing down the cycle. Assume things work out over the next couple of months, the tank gets cycled and the fish are settled. Now you go to do your normal weekly water change and you are having to chase fish away if they come to close to the hose removing the water. You may even be feeding some by hand. The problem now is new = stress levels are greater.
The challenge of doing fish-in cycle is to find the balance between keeping the cycling process moving along as fast as possible while at the same time minimizing any harm to the fish. The only other advice I will offer here is that on any site you will get suggestions which are not uniform and sometimes at odds with each other. This only confuses things. Therefore, I suggest you pick one person from whom to get advice and tune out the rest. Either this person's advice will help you or it wont. But this way you will know what works and what doesn't. This is pretty much how every successful fish keeper has done it.