The center of mass is located at the object’s origin, so all you have to do is move the origin (using ctrl+alt+shift+C in object mode) to wherever you want the center of mass to be.
Sorry, but you can’t have both. Why do you need the origin to be at the center of the object? If you really need to, you can just keep track of where the center of the object is separately.
if you mean that the pieces fall too slow when oress Q is because there too many air friction
“translation” in physic panel
to me seem better keep the value as default(near to zero) then change shape in a box more little(must simulate the arms tha here much more little) and choosing box as shape collision