Welcome to the site. I'm a fellow old timer who has been keeping fish for over 50 years so I understand where you are coming from.
Back in the day, the " cycling process" was called "seasoning the tank" so we have always cycled an aquarium, we just called it something different.
There is no need to use both High pH and Low pH test kits. Unless your Tap water is over 7.8 pH, you only need the low pH test. ( In reality, the high and low pH tests should be reading the same for the lower range so don't make yourself crazy using the high pH test anymore. )
30 + years ago, in most places, the city water systems switched from chlorine to chloramine which is an ammonia/ chlorine combination that is bonded to last longer than chlorine alone so you need to break the bond in order to free the ammonia to be neutralized and the chlorine to dissipate. You need to check with your local water company if they are using chlorine still or chloramine. The Tetra aquasafe is supposed to remove chloramine but I have no personal experience with the product to know if it actually does. From your chart. it appears that it does but you didn't test for ammonia the same day you added the aquasafe to confirm this.
I'm not sure why you added pH down. What is the pH of your tap water straight out of the tap? ( While in the past we used to constantly be adjusting water parameters to match the fish, it's been found to be more successful to match the fish to your natural water parameters since things like the pH will change based on a number of things as will hardness ( GH) and alkalinity (KH) . Most of today's fish are farm raised so their water parameters are going to be different from their wild ancestors. )
To simplify the cycling process, here it is in graph form ( the bottom line is a general number of days. Your experience may/ probably vary) :
The reason they call it a cycle is because the ammonia and nitrite levels start at 0 then go up and then back down to 0. Each one is a cycle but they are usually clumped together and called " the cycle" or cycling process. The ammonia and nitrite levels go down when a nitrifying microbe establishes itself in your system. You need to grow 2 different microbes to reduce both ammonia and nitrites. This process can take anywhere from a number of weeks to a number of months. You will know when you have completed the cycle when your ammonia and nitrites have gone up and down and your nitrate level is rising. (As you see on the graph, nitrates will start to rise before the nitrite goes back to 0 but you need to wait until the ammonia and nitrite levels are back to 0 as well as the nitrate level is rising to be completely cycled and the tank is safe for the fish again.
I surmise that the reason your fish were dying was because the ammonia level reached a level of toxicity that it can kill the fish. As well, the reason your surviving fish got ICK was because they were highly stressed which is all ICK needs to get started. You really don't want your ammonia or ammonia and nitrite combined level to be over .5 ppm to keep the water safe for the fish. While cycling, the way to reduce the ammonia and then nitrites is to do water changes. The plus side of doing this is that it keeps the water safe while the tank cycles.
The down side is that it makes the cycling process longer to complete.
There are now ways of doing " fishless" cycling, a.k.a. cycling the tank without fish present, which is done by adding pure ammonia or ammonium chloride to feed the nitrifying microbes you need in order to keep the water safe for the fish.)
What to do: Obviously your Pure Bacteria pods are not working because you have no nitrites or nitrates after using them. There are a number of products that are " Bacteria in a bottle" but to be honest, most don't work or don't work under all conditions. If I were going to use one of these products, the only one I've found that works is Fritzyme #7. It's not going to be instant cycling but will reduce the time from several months to several weeks. The biggest issue with even #7 is that it has to never have been exposed to high heat or freezing temps. Because of this, you have to be careful where you get this product. I would not suggest getting it in the mail as there is no temperature control that way. It should come from a store you trust. ( But I digress.
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What I would do is start doing water changes to get the ammonia level under .5 ppm. You are going to have to be careful to match the new water to the temperature & pH you currently have the tank at. There are products like Seachem PRIME and SAFE which will neutralize the remaining ammonia by converting it to ammonium which is much less toxic than ammonia for 24-48 hours. With that, I'd do 50% water changes using a product like PRIME in the amount for the whole tank not just the replacement water amount. I would do the 50% change for 3 days which should bring the ammonia level to approx .25ppm. ( You don't want it to be 0 because the nitrifying microbes need ammonia to survive. ) Once you get the ammonia to that .25 range, test the water daily to see when the ammonia rises and do water change percentages accordingly to keep the ammonia level near the .25 but under .50 ppm. Once you see the ammonia level starting to go down naturally ( not from water changes), start testing for nitrites and act accordingly.
I know there is a lot of information here but hopefully it's not too confusing.
