Get yourself a couple of large plastic containers (rubbish bin or storage container). Make sure they are clean and free of chemicals.
Before you do a water change on the tank, put the containers near the aquarium and fill them with tap water. Add enough dechlorinator to treat each container. Add an airstone to each container and let the water bubble away while you drain water out of the main tank. Then fill the tank with the water that has been bubbling away. It will be free of chlorine/ chloramine and you won't upset the filter bacteria.
As others have mentioned, just keep doing big water changes and gravel clean the substrate. A 75% water change will dilute the nutrients by 3/4s and that will make a huge difference. Do a 75% water change each day and the ammonia and nitrite will come down to 0ppm in a few days.
In the mean time, just feed the fish once every couple of days and keep doing daily water changes whenever there is an ammonia or nitrite reading above 0ppm, or a nitrate reading above 20ppm.
In a few weeks time when the filter is working properly, you can feed the fish more often and do a 75% water change and gravel clean the substrate once a week.
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If you want to add something to help speed the filter cycle along, you can buy liquid filter bacteria supplements. Basically filter bacteria in a bottle. Most shops keep it in the fridge.
I normally recommend adding a double dose every day for a week and then pour the remaining liquid into the tank. Try to add the liquid bacteria supplement near the filter intake so it gets drawn into the filter where it belongs.
If you do dialy water changes, then add the bacteria just after you have filled the tank up with dechlorinated water.
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The fish in the pictures don't appear to have any diseases, so if they are dying, it will be from ammonia and nitrite poisoning. The best treatment is big daily water changes to get rid of the ammonia and nitrite.