sorry to say it, but if he will die it not because you was doing salt or water changes. He might die because he is sick unfortunately . You can't say 100% what happened. But i think if you treat something don't stop . Even with people you can't do antibiotic or chemotherapy and stop because person is weak. That is why he has treatment.
And you doing everything you can for him. Unfortunately with bettas you always have that chance when you buy them sick from the store. I had this experience too. I am sure a lot of people are.
Sorry for saying that. Also i think you need a good sleep.