half gallon is still to small, and the tank sizes I'm suggesting are within almost anybodys reach. If you aren't prepared to give your fish a proper home, then you shouldn't be keeping fish. Sorry to sound a little harsh, but it's the truth.
Actually, there is no fish that could live happily in a 1/2g tank. If you have ever seen a full grown betta wich is limited to a very slim number of people(one of mine is aproaching full grown, about 1/2" away) you would agree with me that anything smaller than a 2.5 is way to small for a betta, and a lot of more expierenced fishkeepers will tell you 5g is the min.
As for moving him to his new tank, you should have already cycled a 2.5 for him and got him after that was done, but since you didn't and considering the fact that he's in a little cup where no benificial bacteria can grow or develop, just float his cup in the tank for about 15min. and dump him and the water in his cup into the larger tank.
For food, stick with betta food and add in bloodworms and other insect like creatures(becuase bettas are insectivores), preferably freeze dried or frozen becuase most live foods present a high risk of introducing disease.