A few ideas about basics:

How one stands is the root to movement standing as root of movement:
- Wuji bu is the origin of all Taiji postures. Other stances just variations on the theme.
- The "angle of lateral strength" manifests from Zhan Zhang in the various forms/postures. It is the angle at which the limbs are extended with minimum exertion, and where the core strength of the body can be applied with no overt exertion.
- Apllication of force in this angle is dependent upon observing such rules as "light wrist, heavy elbow", "suspend the crown", etc.
- Spinal management (back opening) is core to rooting, Peng and Fangsong.
- Peng and Song as aspects of same kind of non-specific or non-discrete power (Jin). Peng can be understood as inherent resilience, Song as inherent yieldingness. Their relationship is like a boat floating upon water.
- Weight management on the points of the foot is a source of stability. In applying or receiving force, one avoids having one's weight migrate to any of the three points of the "Triangle".
- Taiji constantly manifests central equilibrium.
- All movement is carried movement and carried movement must follow these principles.

Where's breathing in this?

Not as basic as one might think, since breathing varies in type from style to style, while I believe what is listed above does not.