Re: Breathing & Balance
Breathing helps. Especially during randori and other exhausting exercises. I love watching UFC; you can see when a fighter gets winded because they open their mouth. Anyone who says breathing isn't important hasn't been in a ring for 3 minutes (or their Kenyan j/k).
Breathing technique can get mega-complicated, and I am not qualified to discuss breathing in detail. I rely on basic breathing technique most of the time. Breath in quickly and contract. Breath out slowly (relative) and expand. Then I match breathing to technique; for example, I breath in if my technique is contracting. Most of the breathing I use you can pick up from a good fighting instructor (boxing, wrestling, karate, TKD, etc.) - not to say that you can't get it from aikido instructors too! The important thing to learn to breath comfortably and efficiently. In a combat situation, your mind must be focused on the situation, not your breathing.
There are lots of theories that suggest proper breathing affects your spirit and your posture, which in turn improves your technique. I think there is merit to those theories, but I also think that you have to understand those techniques first. You know what they say, "S*^# in, s$@% out." I know there are good kokyu waza instructors lurking about, so hopefully you can catch one of them.