The chloride ion in salt (or just as well in potassium chloride) inhibits the chloride cells in the gills from taking up nitrite and passing it to hemoglobin in the fishes' blood. --Your nitrites will come, you can be pretty sure.
The dose of salt that will affect a parasite is effective mainly on single-cell parasites and is higher than the fish should be made to live with: over a tablespoon per gallon to 3x that. A long-term salt bath does help cure "fin rot." The fraying of fins on your fishes, OTOH, may be attributable to ammonia. Ammonia is a surfactant: it's breaking up the mucus that protects fish. But it's also an irritant: the fish is making more mucus than a stress-free fish makes. And it's toxic. Water changes will be needed until ammonia is 0, nitrite is 0, and you have some detectable nitrate...