Ravenwinds, had no idea about the freeze dried food being an issue, I've never used it myself, but good to know.
Betta's can go several weeks without food.
And to fix my typo earlier, Hydrogen peroxide decomposes into water and oxygen, 02.
Anyways, as long as he's still alive it's always possible for him to recover, and it sounds like your betta's still got some fight left in him.
I don't fully understand what you mean about it being hot but nowhere to find mosquito larvae. Do you mean there aren't mosquitoes around, or there isn't any nearby sitting water for them to reproduce in? Or something else? If they're around at the very least, put a small bowl or bucket outside preferably somewhere shady, fill it with water and toss a handful of old dry leaves in. You'll have larvae in a week or two, maybe sooner.
Anyways, the erratic swimming and jumping makes it sound a little more parasitic to me. Have you noticed him rubbing against anything? You might try looking at him with a magnifying glass and a flashlight as well, paying close attention to his gills and fins, particularly whichever one he was he was biting at. I think the jumping could be him trying trying to escape from his environment, or from something in his environment that he thinks is harming him, which also makes me think parasite.
Whenever you change his water next, I'd suggest googling a decent how to/dosages for a salt bath and giving that a try as you change the water, on top of what I mentioned before about cleaning the tank with plenty of peroxide and trying a bacterial supplement. Worst case scenario, it doesn't help and you have to think of another treatment. Nothing to lose.