Which area of the brain is most closely associated with sleep and dreaming, as well as coordinating well-practiced body movements?

Answer: The thalamus

The thalamus controls

(a) sensory and motor signal relays (coordination of body movements), such as sight, sound, taste, and touch;

(b) the regulation of consciousness and sleep (sleep/wake) cycles.

The thalamus is located in the center of the brain, between the midbrain and the cerebral cortex.

The Pons area of the brain controls the roll in sleeping and dreaming and also has a primary function of coordination of bodily movements including posture, swallowing, respiration and most other voluntary and involuntary functions. It is superior to the medulla oblongata and anterior to the cerebellum.