Ok, a few things would help your betta out.
As mentioned, bettas are tropical so he needs heat. There are many types of heaters that are affordable.
In a 1/2 gallon tank you should be doing daily 100% water changes. If you want to do fewer water changes, get him a 2.5+gal tank. A large tupperware is better than a 1/2 gal tank. 3 gal Critter Keepers are only $12ish and sold at Walmart. You betta will not get sick as easily if housed correctly. Heaters for larger tanks are also more affordable. The hole looks like the start of fin rot, which is caused by poor water conditions. All you need to do to head off the fin rot is increase water changes.
If you want to feed him bloodworms or brine shrimp, which would be great, get frozen ones. Frozen is much better when you have just 1 betta. You'll never be able to keep large amounts of live food around long enough for your betta to eat them all.
Don't continue the pH additive. Bettas are fine in most tap waters as long as it is between 6-8. Bettas do prefer more acidic conditions BUT if your tap isn't naturally acidic it is pretty much impossible to alter it without stressing your fish.