Should a betta fish filter run continuously in a 1-gallon tank?

If you can adjust the filter flow, it should be fine if you turn it down. If not, you may need to use something to redirect the outflow to decrease current strength. You can use a piece of sponge or pre-filter in the intake to prevent a small fish from being drawn into the filter. Although live food is nice, it can be difficult or time consuming. Live food can be purchased online and typically includes instructions on care and feeding. Food companies all offer "micro-pellets" for smaller fish which is also an option.

The small size will limit the species of fish as well as the number. White Cloud Minnows or Guppies would do fine in a small tank. You could keep no more than 2 or 3 fish total. If you are looking for company for your Betta, the same species can be kept. Other options include Otocinclus (Otos), Corys, Platys or Harlequin Rasboras. Again, no more than one or two in addition to the Betta. Water changes for any tank are simple. Change no more than 30% total volume at a time. Use a water conditioner to remove harmful chemicals and make sure the water is temperature matched to prevent stress or shock. Rinse the filter in tank water, not tap water, to preserve beneficial bacteria. Vacuum the substrate every couple of weeks.

The water temperature should range between 78F and 80F. You can use a submersible heater. Make sure it has an adjustable thermostat to control temperature. You should also have a thermometer in the tank to monitor water temp.

The frequency of water changes depends on how many fish you have in the tank with your betta, how large the tank is (i.e. how many gallons it is), how often you are feeding (more frequent feedings often results in more wasted food and more poop, so it can dirty the tank more quickly), and if you have any live plants present. The amount of salt that is needed also depends on whether you are adding salt just for maintenance or if you are treating your fish for stress or disease. My advice would be to get all of this information and contact your local pet store or aquarium store as they can then help to guide you on these specifics. Alternatively, you can gather all of this information and I can also do a consultation with you as well, whichever is easiest/most convenient for you.

A fish bowl is acceptable but not recommended. Goldfish produce much more waste than other fish. This requires powerful constant filtration and water circulation/oxygenation to maintain adequate water quality. Furthermore, a bowl will quickly become too small for a healthy goldfish. Ideally, one goldfish requires a tank of at least 20 gallons. If you decide on a bowl, you will need to perform partial or complete water changes daily or at least every 2 days. Use aged/conditioned water that is temperature matched to tank water. There are small filters and air pumps that may fit in a good sized bowl to extend the time between water changes. Feed once a day and use a pelleted diet that sinks. Lifespan will depend on tank size, water quality and diet.

Mushu is very cute! Betta care is very easy. Ideally, a 5 gallon tank should be used to house your Betta. A smaller tank can be used, but the maintenance (water changes) will be much more frequent. A filter is always recommended otherwise water changes will be required every few days to maintain water quality. With a filter, 20% water changes can be done weekly or every two weeks. Use only aged or conditioned water that is temperature matched to prevent stress or shock. Choices for conditioners include AmQuel Plus, NovAqua, StressCoat, Prime or StressZyme. A small submersible heater is necessary since Bettas are tropical fish. They do best in slow moving water between 78F and 80F. You can feed a pelleted diet such as Hikari Micro Pellets until he grows bigger. Baby brine shrimp, daphnia, bloodworms and blackworms can also be fed. Feed one or twice daily. He should only need 2-3 pellets at each feeding. The conditioners and food can be found in the aquarium section of the local Petco. Please request a consultation to discuss care in greater depth or post another question in the Forum if necessary.

I would recommend to change his water again and make sure you have a water conditioner that is not expired. I would also recommend to upgrade Smitty to a 3-5 gallon aquarium with a filtration system and a light. These tanks tend to create a healthier environment because the water is moving. You could add in live plants to provide a little extra oxygen. I hope Smitty starts feeling better!