What sort of filter is it?
Please post a pic of the filter if your not sure what type it is.
Most filters have some way to reduce the flow and any filtration is better than none. So if you can get the filter back onto the tank that would help. Filters need to be run all day, every day (24/7). The filter will develop several colonies of good bacteria that convert ammonia into nitrite, and nitrite into nitrate. This bacteria takes around 4-5 weeks to develop but can sometimes take longer.
If the filter is producing too much current when on the side of the tank, try putting it on the back or having the outlet facing an object in the tank so it breaks up the current. Depending on the filter you can put a sponge over the intake tube and that can reduce the current too.
When you have a filter running on an aquarium your should clean the filter at least once a month, To do this you take any sponges or filter materials out of the filter and squeeze them out in a bucket of aquarium water. Once they are clean, squeeze them out in another bucket of aquarium water. Then put the filter materials in the tank. However, do not clean a new filter until it has been running for a week after it has developed the beneficial bacteria.
You can tell when a filter is established by having the water tested for ammonia, nitrite & nitrate. You can buy test kits and monitor this yourself, or take a glass full of tank water to the local petshop and have them test it. Some shops charge a small fee for water testing, this is to cover the cost of the test kits they use.
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Because you don't have an established filter on the tank I would suggest you only feed the fish once every second day and do a 75% water change about 4 hours after you feed him. You can leave the fish in the tank when you do this.
Get yourself a gravel cleaner like the one in the following link. You use the gravel cleaner to syphon water out of the tank into a bucket. While water is draining out, you push the clear tube into the gravel and lift it up. The gravel circulates in the tube and drops back down, while the gunk in the gravel gets drawn out with the water. Use the gravel cleaner each time you do a water change.
You can buy gravel cleaners from any pet shop or online. You just want a basic model like the one in the link below.
http://www.about-goldfish.com/aquarium-cleaning.html
Make sure any new water is free of chlorine/ chloramine before it is added to the tank.
The easiest way to make up water is to get a couple of new buckets and use a permanent marker to write "FISH ONLY" on them. Then use the buckets for the fish and nothing else. Fill a bucket with tap water and add dechlorinator (water conditioner). Aerate the mixture for about 30 minutes and then add the water to the tank.
Aerating the mixture for 30 minutes allows the dechlorinator to come in contact with all the chlorine/ chloramine in the water, and it allows the gases in the water to get to normal levels.
Make sure you turn the aquarium heater off before doing the water change, and turn it back on after the tank has been refilled
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Don't bother washing the marimo ball
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Get a floating glass thermometer from a petshop and put it in the tank. Have the temperature around 24-26C (75-79F).
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re: fish food. Flakes & pellets are the same food, just one is a flake and the other is rolled into a ball. The floating pellets are easier to feed because they don't sink and you can see if there is any uneaten pellets floating around. You want to feed the fish as much as they can eat in a couple of minutes, and then remove any uneaten food and throw it in the bin.
If the water quality is not good, then the fish will be less inclined to eating.
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In the wild male Betta splendens set up small territories about 2 feet in diameter. They chase other males away and try to lure females into their area to breed with them. In a small aquarium the male will consider the entire tank as his territory so you need to be careful about adding tank mates. In addition to this, because you don't have an established filter, you should avoid adding any fish to the tank until you get an established filter on it, and the fish you currently have is feeling better.