API test kits known for false readings. Does not have to be zero but can be < .03 or below.
The fins looked like it has fin rot or has been nipped due to aggression or squabbling with its tankmate and this fish is developing brooklynella which has to be addressed.
That white hazy/milky film is brook and typical clown disease. For temporary relief, you can give it a freshwater bath with temp same as display tank.
As the disease progresses, a thick whitish mucus covers the body. This will usually start at the head and spread outward across the entire body. Skin lesions appear and it is not uncommon for signs of secondary bacterial infections to arise, such as redness and fin rot which your fish is showing.
Best treatment will be General cure which contains formalin. Typically a standard formalin solution is mixed with either fresh or saltwater in a separate treatment container. Initially, all fish are given a quick dip in the formalin at a higher concentration, followed by continued treatment in a prolonged bath of formalin at a lower concentration in a quarantine tank (QT). Of course, the longer the fish are exposed to the formalin treatment, the more effective it will be at eliminating this disease.