On all the three situations that is, holding hands by my side, stretching my hands and holding masses on my hands while rotating, the law applies since no external force is applied. Addition of masses increase the torque under the formula L= Iw where I is a function of mass.
A disk shape produces a low momentum of inertia since it has no hollow space (fully occupied mass towards the center of rotation). According to the equation, and disk process low inertia under free fall than ring given a constant kinetic energy.
As the stool is at rest, angular momentum of the spinning wheel is not conserved since there is an external gravitational force applied due to the weight of the wheel. The wheel comes to rest again. On rotating the stool the angular momentum is conserved since the rotating stool counteracts the weight of the