Thanks thermalEquilibrium. I didn't have enought time to tackle 4 problems but I couldn't say no to the one you left.
97. A conservation of angular momentum problem.
I believe somewhere in Marion & Thornton they show that the angular momentum of a rigid body is the angular momentum of the center of mass of the rigid body (relative to some point) plus the angular momentum of the rotating body about its center of mass.
Taking a positive angular momentum to be pointing out of the page you have the initial angular momentum about the point P to be:
L = -R*v0 + I*w0
(i.e. L = L_of_center_of_mass_about_P + L_about_center_of_mass)
The initial angular momentum is equal to the final angular momentum and the rest is just plugging things in.