Did you clean your tank with any chemicals? Cause if you did, you're not supposed to because it can kill them if you didn't rinse it properly. Anything from simple dish soap can be deadly.
What temperature is his container? Because betta fish become lethargic in cold water. Anything around 80 degrees Fahrenheit is good. Also, when you add new water, is it cold or warm? Use cold water and then warm it up to the proper temperature, because warmer water often takes off the gunk from the inside of the pipes. That's why we're told not to drink warm water, other than the fact warm water tastes gross.
And when you give salt baths, you have to make sure the temperature of the bath is the same temperature of the tank. Any sudden temperatures changes to the water are really bad for betta fish.
For the fin rot, identify it as either bacterial or fungal fin rot. Fungal fin rot will destroy the fin in a uniform manner and/or if there are fuzzy white things growing on him, while bacterial fin rot will attack the fin in random places. Use JFC if it's fungal fin rot, and I'd recommend Maracyn and Maracyn-two in combination if it's bacterial fin rot. If the fin rot gets really bad, I'd suggest you invest in ampicillin.