The most important thing to know about breathing in both the form and applications is to breathe. Sometimes people have an urge to hold their breath when exerting themselves, and, even though this can be tolerated in a certain percentage of the population, I believe this is incorrect.
When I was young I was taught not to hold my breath when exerting myself. From what I've read this is bad because it puts pressure on the heart. Generally, it is better to exhale when exerting effort.
A deep inhale using the diaphragm fills the lungs with air from the bottom up, like filling a glass with water. Some call this "long breathing." The lower portion of the lungs fill with air, air is then brought to the upper chest. Muscles other than the diaphragm, like the intercostals, are used in correct diaphragmatic breathing; indeed some intercostals are interlaced with the diaphragm.
Breathing through the nose is also important because breathing through the mouth can adversely effect the CO2 balance in the blood and cause ongoing mild hyperventilation.
For me there are three ways of breathing during movement in T'ai Chi Ch'uan:
1. Leave the breathing alone
2. Match the breathing to movement
3. Match the movement to breathing
You wrote, > I have a similar question about the Beginning Posture (Qi Shi). If one compares this with similar Qi Gong postures, it would seem that an inhale would be most appropriate; however, if one perceives this movement to be an attack, would not an exhale again be more appropriate? How does one decide? <
When I was taught the long form I was told not try to match them up, that after a while the breathing would match the movements on its own. I was shown the resultant match up: generally, exhale with an outward or upward movement, inhale on an inward or downward movement. In the first move 'The Arising' I was taught to take a deep breathe and begin. The hand go upward and outward with the exhale.
In some schools this is reversed. In a movement like 'Cloud Hands' when one hand rises the other falls, while one goes in the other goes out, so the breathing is more a matter of timing than direction.
Matching the movement to breathing is simply a drill, but it can be difficult because you have to pay attention to your breathing without changing it. This has to do with the open/close aspect of Tai Chi. If you leave your breathing alone and move with it, you may be able to feel the ebb and flow of the energy. Allow the movements to be smooth and even, and move as though you are in deep water moving back and forth with the tide.
> If multiple breathing patterns and principles are acceptable, why bother choosing any particular one?
Because of the consideration of effectiveness and what suits your body.
> If one has a fixed pattern for the barehand form, is this same pattern applicable to performing the form at other speeds? If not, why should the principles change? <
If the oxygen intake requirement changes your breathing must change.
> What do you do when you are forced to form at another?s pace? Should you match their breathing pace even if this is not completely comfortable? <
In such a situation, unless matching breathing is part of the drill, leave your breathing alone.
> What about weapons forms and push hands?
You need to breath during them too.
I hope this helps.