Answer
a. No, the momentum of the ball alone is not conserved during any part of the process.
b. Yes, now that we include the Earth in the system, all of the forces are internal.
c. The answer is unchanged.
Work Step by Step
a. An external force, gravity, acts on the ball at all times. Also, during the collision there is a strong, sharp upward force acting on the ball. So if the ball is the system, there are always external forces, so its momentum is never conserved.
b. The momentum of the Earth-ball system is conserved during the entire process.
c. If the system is the blob of putty and the Earth, the total momentum is conserved during the entire process.
