No need to jump on him...at least he is here looking for proper advice.
Well, first up: welcome to the forum!
1 gallon is fine for a single betta, provided you're willing to so several weekly water changes-though most people recommend at least 2.5 gallons for each betta.
Heaters are definitely needed, since bettas are tropical fish.
So before you try anything, I would focus on getting one more tank for the betta and two heaters. Those two definitely need to be seperated. The tank is far too small and you didn't go through the proper procedures for breedng them. If you leave them together, they will kill each other-the male is already looking pretty beat up. So, I think that the priority should be seperating these two bettas and treating the male.
Secondly, breedng takes A LOT of work-it requires tons of research, space, money, and time. There's a lot of thought and consideration to be put into it. It's not as simple as plucking two bettas in a tank and hoping for the best-so, I would advise you to focus more on fishkeeping for now and breeding later when you're more experienced.
Hope this helped.