When I empty out intentions and relax in meditation, what is this force that moves my body in complex patterns? When I empty out intentions and relax in meditation, what is this force that moves my body in complex patterns?
For example, when I let go for a bit I start walking and making circles and doing movements with my hands (mudras), and even martial arts type of moves with intricacy and  intelligence. There is a force making me doing it and I feel my body following energies like a magnet.
So the questions are:

why does it happen?
what am I suppose to do with it?
is this like wu wei of taoism or Tibetan Buddhist Shamans channeling spirits?
That's chi, not wu wei.  Wu wei is more of an approach - one that can give rise to feelings of chi, aid in samatha meditation, etc.  Using chi is outside the scope of Buddhist practice, although Jwing-Ming Yang mentions its role in Buddhism in many of his qigong books.  Personally, I appreciate his effort, but his writings on the subject seem like a bit of a stretch to me.  You're better off just sitting on the cushion.  Meditation practice is complicated enough.  No need to add additional complexity.