Pellets are very important for a staple, they have all sorts of nutrients and good stuff in them. If she won't eat one brand, try another. Crushing them up is a good idea if they're larger, or even soaking them would be good...even though it gets bigger when you soak it, she could pick it apart easier. From what I've been told, flakes aren't a good staple because they contain a lot of plant matter and Bettas are carnivores....so its not so good for their digestive system. Se if you can snag a couple different pellet brands when you go out next to try ;)
Hikari brand frozen food is the best, very well sterilized and safe. I've never once had any issues with my frozen food. What you need to watch out for is the live food, thats where the real danger of parasites and such are. Though, again, its up to your preference as there is a lot of conflicting info out there.....though I will always advise frozen over freeze-dried. But yes, definitely soak the freeze-dried before feeding....10-15 minutes in a little cup of tank water should e good :)
I'm afraid I'm not so good with diseases.....that a whole lot of experience in that field. Though a picture would help greatly, its difficult to say what it might be without one.
As for the swimming.....does it happen when your over on that side of the tank? She may just see you...as for the stress stripes, I'm not sure on that one. My girls are funky and show stripes at the most random times, I'll never figure them out.
If she just does it at random when your not on that side of the tank, then she might see her reflection, or something next to the tank shes trying to get at....just be sure to provide lots of plants and a cave or two in the new tank so she doesn't feel exposed :)