First on the platy, this is due to the water. Nitrite at 1 will kill the fish, and gasping for air is undoubtedly due to the nitrite. Nitrite affects the blood preventing it from carrying oxygen, thus the gasping. This sounds pretty far gone, so be prepared to lose the fish; no fish can survive this. Just so you know what to expect.
The cycling article Geo linked previously will explain this. I use live plants to avoid cycling issues, something as basic as floating plants will work.
On the pH and hardness, are you sure the GH is zero? This alone will severely weaken the platy (all livebearers need harder water) and leave it vulnerable. Perhaps you can contact your water supply people, they may have a website, and ascertain the GH and KH (Alkalinity) from them so we are certain and will know how to deal with this.
And the high KH is what is preventing the pH from changing, Alkalinity works to buffer pH. For some background, have a read of this: http://www.tropicalfishkeeping.com/f...quarium-73276/
And as Geo said, any chemical added to the water will have little effect, and all these also stress out fish, further weakening them.
Hang in there, we will sort all this out.