I have a betta as well, and in fact have always had a betta at one time or another in my life.My betta actually does similar to yours when it comes to the food, he is young though, he used to swim down and get the bits as they fall, now they seem to get away from him.I have started using floating food, which he seems to like, and takes off the surface as he wants it.As far as the favoring of one side I couldn't tell you really, mine have never done that.This is a very very good site in reference to Bettas though:
http://www.bettatalk.com/FAQ_library.htm