[ao]

Ive had bettas with similar syptoms. It is usually a sign of a fragile immune system. he will most likely need pristine water conditions to recover. for a .5 gallon, you should probably do daily 100% water changes. I recommend to be able to heat his tank.... if he isnt eating, dont worey about food for now...

 

[ao]

you can use 1 part bleach to 9 parts water to sterilize,
after you do that soak it in water with extra dexchlorinator. I would usually let this sit for a night. but the dechlorination should be instant...