If you have an established filter on the aquarium, then you should do a 50-75% water change and complete gravel clean each week. Any new water should be free of chlorine/ chloramine before it is added to the tank.
To clean the substrate/ gravel, use a basic model gravel cleaner like the one in the following link.
https://www.about-goldfish.com/aquarium-cleaning.html
An established filter is one that has developed colonies of beneficial bacteria that eat ammonia and convert it into nitrite, and more bacteria eat the nitrite and convert it into nitrate. It takes about 4-5 weeks for this good bacteria to develop in the filter and during that time you get ammonia and nitrite readings from the tank water. Any ammonia or nitrite in the aquarium water can harm the fish so a lot of people try to cycle the filter before adding fish. Cycling a filter is letting it establish (develop the good bacteria) by adding liquid ammonia or a small amount of fish food, and then leaving the filter to run continuously until the bacteria have developed in a month or so. This is known as a "fishless cycle" because the filters develop without fish in the tank.
You can also do a "fish in cycle", where you have one or two fish in the tank and only feed them a small amount once every few days. You do a 75% water change about 4 hours after feeding the fish and this helps keep the ammonia levels low enough so the ammonia doesn't harm the fish. After about a month the filters have developed the good bacteria and more fish can be added to the tank.
Most people on here will tell you to do a fishless cycle, whereas I do fish in cycles and keep the feeding down. A fish in cycle lets you have fish within a few days of setting the tank up and that means you have fish sooner. The main drawback to a fish in cycle is you have to do lots of water changes to keep the ammonia and nitrite levels low, and this means more work for you.
If you do a fish in cycle you can add liquid bacteria to help get the filters going quicker. The one I use is "Sera Nitrivec", but there are others brands available too. You add a certain amount of the liquid bacteria as recommended on the bottle and it adds beneficial filter bacteria that are in a dormant state and these activate in the water and take up residence in the filter. I add mine to the aquarium near the filter intake so the spores go into the filter rather than into the tank. These products can be helpful but you do not have to use them.
There is more information about fishless cycling and fish in cycling at the following link.
http://www.fishforums.net/threads/cycling-your-new-fresh-water-tank-read-this-first.421488/
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Yes, a marimo moss ball be kept in a Betta's tank.
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I don't recommend tank dividers. I prefer individual tanks for male Betta splendens (Siamese fighting fish). The males sometimes jump the dividers and get into each others compartments. And living with another male next door, where both fish can continuously see each other is stressful to the fish as they remain in a constant state of fight or flight. And since they fight they will spend all day showing off, which looks good to us, but is bad for them.
Separate tanks for males and have a piece of cardboard between the tanks so the fish can't see each other. Then once or twice a week you can remove the cardboard for 30minutes or so and let the males fight through the glass, then put the cardboard back. The males will think they drove the other male away and will strut around like a proud rooster for a while before settling back down.
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Breeding:
During breeding the male will build a bubblenest on the surface among some floating plants. It's called a bubblenest because the male takes in air from the surface and puts a mucous coating over an air bubble and uses this to build his nest. The water surface needs to be fairly calm/ stationary for the nest otherwise it will break up. The best floating plant for Bettas is Water Sprite (Ceratopteris thalictroids). This plant can float or be planted in the gravel. They need it floating for their nest.
When he has built his nest he will wait for a female to swim by and show off to her. If she has eggs and is ready to breed they will lay a few eggs in the water and the male will pick up each egg in his mouth and coat them in mucous/ saliva and stick them in his nest. This continues until the female has expelled all of her eggs. Then the male chases the female away from the nest and looks after the eggs and fry (baby fish) for the first few weeks of their life.
The female should be carefully remove after she has laid all her eggs otherwise the male might attack her. Some males and females can remain together but you have to watch and monitor the individual pairs and if there is any aggression then separate them.
After a couple of weeks the male will show less interest in caring for the fry and this is when you remove him.
When the young fish are starting to mature (around 2-3 months of age), the young males will start to show off and fight with each other. This is when you separate them. The males go into separate containers and the females can remain together in one container/ tank.
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You can get Bettas from any petshop, online at place like Ebay, Gumtree, Craig's List, Aquarium Societies, and even some stock feeders sell them. There are numerous colours and fin types so look around and don't buy the first one you see, because there will always be a nicer one just around the corner.
