Stocking levels in tanks have nothing to do with how long it takes a tank to cycle. On average it takes about 4-6 weeks for a filter to cycle and the development of the filter bacteria is directly linked to the aquarium and environment. There are filter bacteria (and hundreds of other types of bacteria, yeast, viruses, fungus) in the air around us and it takes time for the beneficial filter bacteria to settle into an aquarium and start growing. If you have an established aquarium or pond near the house, there will potentially be more filter bacteria in the air that can settle into your tank. However, if the house is kept really clean and the windows and doors are shut, not many filter bacteria will get inside the house and even fewer will get into the tank. Coverglass and hoods on tanks can also reduce the number of bacteria that get into a new aquarium.
Adding liquid filter bacteria in a bottle can help speed things up because you are adding dormant filter bacteria to the water and they quickly wake up and start multiplying. When their numbers build up to sufficient levels the ammonia and nitrite levels will drop pretty quickly.
Adding live plants, gravel or driftwood from an established aquarium can introduce some beneficial filter bacteria into a tank. However, it is only a small amount and will take time to build up in numbers. Liquid bacteria in a bottle is quicker.
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If your fish have a disease (protozoan parasite) that is causing the irritation and rubbing on objects, then they will get worse without treatment. So if you stop using salt and dilute the salt out with water changes, and the problem hasn't been cured, then it will get worse.
Most pet shops don't appreciate being given sick fish so if the fish have a disease (as opposed to ammonia irritating them), then the shop won't be real happy if you give them diseased fish.
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Just leave the fish in the tank, do water changes, and keep the salt level up unless you see some other symptoms like white spots or something else.
Reducing the number of fish in a tank won't lower ammonia levels that much. Fish food adds most of the ammonia and if you only feed the fish a couple of times a week, there will only be a low level of ammonia in the water.