Bettafix is bad, it contains tea tree oil which can coat his labyrinth organ and suffocate him.
He needs to have a consistent temp. Your light schedule and food are OK, but you need at least two water changes a week in that small of tank - a 50% and a 100%. It is probably why he's sick and he probably won't get better if you don't up the changes. Clean, warm water should help his fins and its the first step but he may have a bacterial infection and a fungal infection. I would treat it with Kanaplex - kill two birds with one stone.
Start with aquarium salt, predissolved (important) added slowly to 1tsp per gallon up to 3tsps per gallon. Use Indian almond leaves if you can. Cover the tank with suran wrap with holes in it to increase humidity and help with his labyrinth organ and remove the bettafix with a 100% water change. Add stress coat at a double dose to help his fins and get VitaChem if you can.
I'd change the water ASAP.