Your water conditioner (API Tap Water Conditioner) is fine. You need to do more frequent water changes, though. You are only changing 25% per week, and you have no filter. It's likely that the ammonia and waste levels are high in your tank.
The water change recommendation for a 3 gallon tank with no filter is one 100% and one 50% water change every week. That said, if you have live plants, the recommendation would change since they would utilize the ammonia as fertilizer. Here is the water change recommendation thread: http://www.bettafish.com/showthread.php?t=115758
It's not necessary to add aquarium salt. Bettas are sensitive to salt. Using it for long periods of time can harm their kidneys. I would try keeping him in clean water, without added salt, and seeing if the fins heal.
Also, I agree with Callistra's food recommendation. Look at the ingredients on the food container. The first several ingredients should be fish proteins. If they aren't, consider getting a higher quality food. The two more frequently recommended foods on this forum are New Life Spectrum (NLS) pellets and Omega One Betta Buffet pellets.
Thank you so much! I just changed out his water and my female's water as well. I have to be particularly careful with my tap water because sometimes it gets bad. Like it turns brown from time to time. It's really annoying. Luckily I changed the water before it decided to turn brown again.
Brown? Is there a high iron content? Or is it some type of sediment? Are you on municipal (public) water, or well water, etc? If you're on municipal water, have you asked them the cause of the discoloration?
Brown? Is there a high iron content? Or is it some type of sediment? Are you on municipal (public) water, or well water, etc? If you're on municipal water, have you asked them the cause of the discoloration?
It might be some type of sediment. I live on a military base and there will be a time where a pipe breaks and has to be fixed somewhere in the residential area.