Also, for problem 21, I know that in the collision, kinetic energy and total momentum are conserved. However, linear momentum and angular momentum are not conserved. Consequently, I'm having trouble getting enough equations to solve part B. Any suggestions?
Your exact choice of words above has me worried. I agree that kinetic energy is conserved. In addition, total linear momentum is conserved and total angular momentum is conserved, each independently. The phrasing that you have chosen suggests that you think that this is not the case.
Although it is true that you must add together the linear and angular contributions to energy to make a valid law for conservation of energy, it is not true that you must add together the 'linear' and 'angular' momenta. In fact, adding together a P and an L gives nonsense -- the dimensions aren't the same. They are two independent conservation laws, both of which are valid for this problem.
I recommend that you choose an x-y coordinate system with the origin at the center of the stick. If, in addition to writing down teh consequences of conservation of energy, you also write down the consequences of conservation of P and the consequences of conservation L, then you should be in pretty good shape to solve the problem. That will give you three equations with which to solve for the three 'effective' unknowns of the final linear velocity of the stick, the final angular velocity of the stick, and the mass m.