Would I be able to keep one male and one female betta in a 15 litre hex tank?
(without them breeding)

that would be hard so i would say no, just get 2 females... or 2 males... this tank has to have oxygen for them/filter.

Would you be able to put a cat and a mouse inside a cage without the cat eating the mouse? I guess you can't fool mother nature

YOU CANT KEEP TWO MALE BETTAS TOGETHER, THEY WILL KILL EACH OTHER!!!!!!!!!!!!!

PearlscaleFan maby you can get a tank devider to keep the male and female from breeding