yeah, in a half gallon you need daily 100% water changes.
you also need a heater, regardless of where you live, to keep the temp stable because temp fluctuations can be harmful for your bettas health.
I personaly would just get him a 3-5gal, a heater, some plants and a filter, thats all you need, and after a few weeks (when its cycled) youd only need to change maybe 30% of the water every week. all of my bettas have about 5 gals, its really a nice size for them, although i wish i could just give them their own 10gal, they really do use, and love all of their space.
i notice yous bettas fins look a little choppy, it could be from thooose plastic plants, id suggest some silk, or easy live plants, and i would be happy to help you out by telling you that info if you need it:)
I really only want whats best for your betta. trust me, earlier this year I started with one small betta in a .75g unheated tank, when I was trying to figure out why he wasnt eatting, I came accrost this webiste, it literally saved my bettas life, whom now happily resides in a natural planted 5.5g alllll to himself!:)
please read theese:) they are helpful! http://www.bettafish.com/showthread.php?t=115758