heres the catch. the tank should be a bare tank that means there are no airstone or any gravel. thats the # 1 standard rule for betta keepers.. why?
first of all bettas do not need oxygen in the water since they breath air ... whaatt?? nooo airrrr??? thats right .. they breath atmospheric air they dont depend on the oxygen in the water. having a bare tank means cleaning more easy, since you have a 2 gal tank for the betta, use a cup to capture the betta then clean the whole tank then put the betta back ones the tank is clean, thats how you do it
and having a brown algea is just to much for a betta tank
have fun and enjoy