I didn't see any fuzz in the pics..The white on his lower head? Its normal coloring. Mr Mushrooms has it too. Or is there something that actually looks like fuzz growing on him? And no, I do not keep him in a cup. He was getting a water change
many people do use 1gallon tanks as hospital tanks - makes it easier to do the 100% daily water changes that are usually required. Many bettas live in larger community tanks or in tanks with other species that can not handle salt or some meds
New life spectrum and omega one pellets seem to be the best. You can also skip a day of feeding which helps the digestive track. If you want to use flakes - go with omega one. They are larger so its a bit harder to overfeed. also if the bloodworms are freeze dreied - soa it in water for a few minutes before feeding. That way it will already be expanded before the betta eats it.