First of all, female bettas CANNOT be kept in the same tank with male bettas. The male will attack the female if they're kept in close quarters. At the very least, a male and female will nip each other's fins if kept together. Breeders keep the males and females separated until it's time to breed, and then separate them once again after breeding. Female bettas can be kept in a tank with other female bettas, though.
I've heard that tetras get along fairly well with bettas, but it depends on the personality of the male betta. Some bettas are very aggressive, and some are not very aggresive at all.
It may be possible to test his personality by showing him a mirror and seeing how he reacts. I have one betta who flares, darts, and rams himself into the side of the tank when he sees his reflection. But when my other betta sees his reflection he flares a little, but eventually retreats back into his tank and goes about his business as usual after awhile.