A Wonderful Dream

Bengt is asleep in his bed, dreaming. In the dream he is in free fall with no air friction. It is almost dark; the only things visible are Bengt's glow-in-the dark watch, which shows that he is not supposed to wake up for another six hours, and a brightly glowing point of reference far away.
"What a lovely dream!" thinks Bengt. "An endless, homogeneous gravity field. The perfect opportunity to perform a really incredible twist... jump, or something. By moving my arms, I can make myself spin around and around."
Suppose Bengt's body is a cylinder, with height 1.8 m, radius 0.25 m, and mass 90 kg. His shoulders are represented by massless spheres, with radius 0.05 m, attached to the body on opposite sides. His arms are also cylinders, with length 0.8 m, radius 0.05 m and mass 5 kg each. The base of the arm-cylinder intersects the shoulder-sphere, dividing it in half, and spins around it.
He lets his left arm point forward and his right arm straight out to the side, then he moves them 90 degrees to the left, and then he brings them down parallel to the body. This he can repeat once per second.

1. If Bengt's mass is constant, what angular speed can he reach before waking up? (Assume that he can take any angular speed without expanding or exploding. It is a dream, after all.)
   
   
2. If the gravity is the same as on Earth, how far will he fall?
   
   
3. If all the energy needed for the rotation is taken from fat in his body, how much lighter will he get? (Assume that the fat is homogeneously distributed in Bengt.)
   
   
4. If he finally lands in his bed without bouncing back up, what change in velocity will the Earth get?