3 months should have you cycled, but we are where we are.
Im going to start off with why your fish are dying. And then
go on to why i think your cycle hasnt established.
It seems you understand that when you arent cycled you need regular water changes to remove waste because you havent built up enough bacteria to consume the ammonia your fish produce. But, you havent been doing anywhere near enough water changes. 5+ ppm
nitrite is very high. At that level it will be causing long term health issues and possibly short term deaths as well. You really need that below 0.5ppm. Based on it being 5ppm you need to do 4 back to back 50% water changes. If its much higher than 5ppm you might need more. Do them an hour or so apart, test 20 minutes after each water change. Once its down to around 0.5ppm retest 24 hours later and see where you are. But, dont do that just yet.
Quickstart isnt a dechlorinator. It is a product that "supposedly" contains bacteria that consumes ammonia. It doesnt remove chlorine or chloramine from your tap water. So before you do those water changes you need to make sure you have a dechlorinator. Are you sure its called quickstart? A lot of products have similar names and are easily confused with each other. Ill also come back later to the "supposedly".
With nothing removing whatever your tap water is treated with (chlorine or chloramine) that water treatment will be killing the microbes you are trying to grow. Every time you do a water change you will be starting your cycle over, or at least setting things back a little. Chlorine or chloramine will also be causing long term harm to your fish and killing them.
The "supposedly" is because most of these bottled bacteria products in reality arent likely to do anything useful. Even if they do have bacteria in there, most products contain the wrong bacteria, and even if they do contain the right bacteria, if they havent been stored and transported in temperature controlled conditions the bacteria just dies off. Save your money and stop buying quick start. There are better products available if you want to go down the bottled bacteria route if thats your wish.
So. Have a read through above. Just confirm what products you have. When we are sure you have a dechlorinator do those water changes. We can then look at making sure you cycle your tank in a safe manner.