Do you have pictures of your female? That will help us determine her tail type.
However, how long have you had her? When bettas reach the pet store for retail sale they are usually already 4-6 months old. So if you've had her for a few months she could be too old to safely breed right now. I wouldn't breed any betta over 10-12 months old.
No, you cannot keep a male and female betta together. In the wild, the female would have plenty of space to get away from any male who was unwilling to share his space, in a tank she would be injured or killed. Yes, you can have a female sorority. In your 12 gallon tank you can do up to 7 or 8 females if they are the only fish in the tank. You would need to heavily plant it and provide them with lots of caves to hide in if need be while they establish a pecking order or hierarchy. This can be the defining point of a sorority's life, the females will either nip and bicker until they have established a hierarchy or they may attempt to kill one another.
If you want to breed bettas you'll need a heated and gently filtered cycled 10 gallon tank, half filled with water, lot of plants/places for the female to hide if needed, live foods for the fry and to condition the pair you're breeding, a grow-out tank of at least 20-30 gallons (also heated, gently filtered, cycled), and space for lots of small individual tanks to separate the males when they start to get nippy with their siblings.