First: The mossball doesn't effect water parameters measurably. Neither do Anubias, Java fern, Java moss or other slow growing plants. Anacharis, Wisteria, Water sprite, Water lettuce are NON-root-feeders that eat ammonia and nitrate. Swords, Crypts, Hornwort and heavy root-feeders will definitely benefit water quality---while adding plant maintenance to your schedule.
Your cycle is proceeding faster than most. From your high nitrite readings, I'd say cut back on your ammonia...1.0ppm is plenty at this point. Keep the nitrite and nitrate below the maximums. You're almost cycled.
Some Betta like peas; most don't. In any case, carnivores (insectivores, actually) shouldn't have much vegetable matter in their diet. Most of what they get naturally is from gut-loaded prey.
A good-quality pellet, like NLS or Omega One contains enough roughage for good digestion. Frozen Daphnia will also keep them regular.
An occasional frozen (not freeze-dried) bloodworm for protein. It's nice to know that he'll take a pea-laxative should he ever need it. A proper diet and not over-feeding will preclude the need.
You were intelligent (and compulsive ;-} ) enough to keep a log. It's a great learning experience. Would you be kind enough to share it with us on this thread?
Thanks, JA. I'm sure we'll all benefit from your input.