He doesn’t need a filter
His waste is obviously being used by the plants and especially algae
50% water change each week will be enough
Temperature is very important 25 minimum
At lower temperatures they are less active
Bettas will not just display to a mirror on command, it’s a training programme and it’s takes up a lot of energy on their part
He looks like a veil tail and dragging those long fins around takes up energy
He needs good quality food designed for a betta or live food such as daphnia, you will enjoy watching him hunt them down
He also needs somewhere to rest ideally at the surface
My advice is
More plants
& add Floating plants
Heater
Good food
50% water change each week
Be patient with the mirror banging it at the walls for a few seconds is just going to stress him
Look at possible tank mates, I strongly believe fish get bored and possible lonely and depressed
I suggest without a filter adding some nerite snails, and shrimp, the larger species, glass shrimp or amano
If you want smaller colourful shrimp then neocaridina species such as red cherry etc don’t expect them to breed though as your betta will hunt and eat the babies
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