Yes. It is best practice to always have the aquariums filter running. In addition to removing impurities it also promotes a fresher ecosystem for the fish as the water is moving and won't grow stagnant
Short answer, yes. Since the water in an aquarium does not have natural filters to remove bacteria and things that will make the fish sick, you need to leave the filter dunning 24/7. The only time it should be off is for short periods of time when the tank and filter are being cleaned.
The real fact is goldfish can live without filters. However, it will shorten their life span. The best way is to let them live in a huge tank with filter.
No, the filter does not need to operate permanently. It should be turned on for at least six to eight hours a day to keep water clean and provide the goldfish with adequate oxygen.
The belief that goldfish need a filter is incorrect. Goldfish don't actually need filtration and can live long lives, as you may have seen, without filtration. The longest-lived goldfish, Tish, lived to 42 years old in a regular fishbowl