The others have answered your questions pretty well, but I will add that the bigger the tank, the better. I would suggest no less than a 2.5 or 5 gallon tank. The more room they have the more active they will be.
Also try to avoid filters - the water disturbance can stress them out. Though the water disturbance is not as noticable in larger tanks, so if that is the case then you can experiement and observe him a few days just to see.
Also if you DO decide to get a larger tank, bettas DO make wonderful tank mates with other types of fish, contrary to popular belief. They just do not get along with other aggressive type fish, any other bettas, fin-nipping fish, or any colorful fish that could be mistaken as another male betta.
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