Where does yinyang symbol come from?
The Yin/Yang symbol comes from Taoist texts and diagrams, based on the I-Ching. It reflects the dual nature of all things, according to Taoist philosophy.

Why do we practice Tai Chi Chuan in slow motion?
Tai Chi Chuan is practiced in slow motion to establish body control and active mental control of bodily motion. This is generally more difficult than faster motion since the body control must be exercised from one movement to another and body momentum is not a great factor. This trains the body and mind to work as one, to maintain balance when moving and to keep relaxed during the motion.

Is there a simple sitting qigong I can start the day with?
Yes, please see this Five-minute Qigong.

Where can I find medical research about Tai Chi/Qigong?
The World Tai Chi Day web site has a large collection of references.