Thank you all who sent their ideas, musings, and comments. You will see we tracked on many items! Here is my rather long answer from my meditations and ponderings, and thoughts on training techniques for practical use.
During a thirty-minute round of Tai-Chi, I am working on my alignment with gravity, and the careful transfer of weight from foot to foot and leg to leg. Paying attention to where and how my center of gravity moves. This culminates in training my balance.
From the beginning to the end of my round, I am constantly checking my relaxation and seeing if tension shows up in jerks, inconsistencies, shallow breath, forgetting the sequence, and losing balance. Relaxation is the key to speed in martial arts, sports, music, etc.
Breathing with my nose and not my mouth and starting and ending each breath with my lower abdomen, helps with proper oxygen levels. I want to neither over breath nor under breath. Breath keeps me calm, maintains my energy levels, and helps with endurance at my age.
For thirty minutes I work on coordinating the upper and lower parts of my body. Using the principles of start together/stop together, and having my whole body as one unit, I work on my whole-body power. Power in Tai-Chi comes from the harmony of the 9 Joints and the whole body unified in any action.
Using my mind to direct my body, practicing meditation in motion, I work on my intuition, instinct, and will-power.
There are so many turns, shifts, bends, circles, and sinking in thirty minutes of solo form practice. These are the foundation of the Willow exercise and the defense in pushing-hands.
So what am I working on and perfecting for a thirty minute round? I am working the whole time on Balance, Speed, Power, Endurance, Defense, and Will-power! That is my answer.
As for techniques for mastering for sparring and self-defense, although there are some great techniques in the solo form, most are for a very narrow set of circumstances. If you think you are going to use Single Whip while sparring or fighting, you will probably end up like the modern Tai-Chi masters who are getting beaten up.
I suggest four techniques to master for sparring, Fair Lady, Parry and Punch, Brush Knee, and any of the front kicks. Remember big moves in training become small moves in fighting. Do these four at least a thousand times in the air, then another thousand against a bag.
Then, practice defending against single punches and kicks. Then practice kicking and punching at a moving, non-compliant opponent. Then try offense and defense together. This is how you learn how to fight.
Just doing solo form, or pushing-hands with a willing partner, is not enough training. Just my experience and opinion. Namaste!