The brown and green stuff on the sand looks like blue green algae (Cyanobacter bacteria). It can lift off in sheets/ pieces and smells musty. It is a photosynthetic bacteria that loves light, nutrients, low oxygen levels and still water. It regularly grows in aquariums that have lots of uneaten food or where dry foods are used.
Try doing a daily gravel clean and water change to suck out as much as you can. Make sure any new water is free of chlorine/ chloramine before it is added to the tank.
Reduce feeding and try to use live or frozen (but defrosted) foods instead of dry food. You can still feed dry food but only offer a small amount and remove any uneaten food after a couple of minutes.
If the tank has been running for more than 2 months, clean the filter if it hasn't been done in the last 2 weeks.
Old light, particularly fluorescent globes can encourage this. Fluoro globes above aquariums should be replaced every 12 months. Try to use globes with a 6500K (K is for Kelvin) rating.
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It looks like you have a water pump/ power head in the tank and that should be providing sufficient water movement. I would look for a round/ cylindrical sponge to go over the intake strainer of the pump so sand doesn't get sucked in and damage it. Most pet shops sell round/ cylindrical sponges for some brands of internal power filter. Just find one that fits over the intake strainer of your pump and put it on. They get held in place by the suction of the pump.
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You should put a picture of something over the back of the tank to make the fish feel more comfortable. You can buy aquarium backings (plastic pictures) from pet shops or use a plastic bin liner, newspaper or coloured card. Dark colours are best. Just sticky tape them to the outside of the tank and the fish will feel more secure.
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Water Sprite (Ceratopteris thalictroides/ cornuta) is a good plant for Bettas. It floats on the surface and grows rapidly. If you get too much on the surface you can plant it in the substrate where it grows into a lovely light green shrub.
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The water in my area is very hard, so I put an IAL in to try and combat the hardness for my betta.
I'm not sure what this is.