Males shouldn't live in coldwater temperatures it is unhealthy same with females. Gender doesn't change it. They should have atleast 1 gallon and you should clean bowls weekly unless they are under 1 gallon. Only some bettas and very few at that are scared of larger areas to swim and they will usually get used to it. I once had my betta Risteek (RIP) in a 10 gallon to him self and he loved it.

Good luck.