A 2.5 gallon tank with ONE fish needs one 100% and one 50% water change per week, as others have pointed out. You have two fish in there, so the ammonia and toxins are building up very quickly.
Since the water is only changed every two weeks, the fish are swimming in their own waste. Basically, they're living in a toilet that hasn't been flushed. (Yuk!)
Using a filter every other day isn't going to do much. It may help draw out a little of the waste, but it's not going to take the place of doing frequent water changes.
Using bottled store brand drinking is fine. But don't use distilled water! Drinking water and tap water contain dissolved salts that fish (and people) need. Distilled water doesn't contain these. Regardless of whether you use bottled drinking water or tap water, you should always use conditioner that removes chlorine, chloramines and heavy metals. (Often, these conditioners also contain chemicals that protect the slime coat on fish, too.)
Don't worry about the pH of the water. Bettas can handle a pH wide range. If it's safe for people to drink, it's OK for your fish.