The heavy breathing could be a sign of parasites, did you quaretine the fish before putting them in the tank? Maybe
@Jay Hemdal can help, but unless it was showing other signs I’m not sure how easy it will be it figure out.
API is a crap test for ammonia. It always reads .25 for me whenever I used it in the past. This could be it. Maybe try a different ammonia test kit.
The easiest way to run carbon is put it in a media bag. Then you can throw it in your filter, or in the tank if need be, but it would be best it a filter. What filter do you run?