The white stringy poop and the lessened appetite is indicative of intestinal parasites. I would definitely feed food soaked medication for that issue.
As far as the breathing goes it could be many different ailments. Clowns can be hard to diagnose. They can carry velvet without any visible "spots" etc. Due to the very thick mucus layer. I would recommend a FW dip. This is one of the reasons I choose to prophylactically treat my fish, because certain fish especially Wrasse, gobies, damsels etc. Can carry parasites in gills without external symptoms.