Hello Sashimi! I've only had my angelfish for about a month, so I don't have that much experience with them, but I've read a lot on them. So I'll try to answer some of your questions, if you don't mind a bit of a newbie answering them.
First of all, from what I've read your tank would be too small. Angelfish grow to be quite large, with an average size of 6 inches tall, though they can grow to be 12 inches, but this is rare. One site reccomends if you keep angelfish, to have a tank that is at least 20 inches tall as they like to swim up and down a lot. Another site recommends a size of at least 29 gallons, as they like to be kept in groups of 4.
The reason fro this, is in groups of 2-3 the larger more powerful angelfish tends to bully the others, make life miserable for them.
Also, from what I've heard Angelfish usually don't do well with bettas, because they can nip them, and angelfish can be agressive sometimes. (remember they are a type of cichlid). It all depends on the size of your tank, wether they'll co exist peacefully or not.
Lastly Angelfish are omnivores, they do prefer the flakes, and freeze dried blood worms, but they like havign black worms and brine shrimp soemtimes.
So really, even though Angelfish are beautiful, I wouldn't recommend buying them unless you get a bigger tank. Especially if you keep them with your betta. Really the only reason I think mine are getting along well with my betta, is because of how big my tank is.
(sorry if this isn't what you wanted to hear