Conservation of angular momentum is a consequence of Newton's 3rd law, so anywhere where Newton's 3rd law doesn't hold (such as in systems with external, unbalanced forces), angular momentum need not be conserved. read more
Angular and linear momentum are not directly related, however, both are conserved. Angular momentum is a measure of an object's tendency to continue rotating. A rotating object will continue to spin on an axis if it is free from any external torque. Linear momentum is an object's tendency to continue in one direction. read more
Because angular momentum is the product of moment of inertia and angular velocity, if the angular momentum remains constant (is conserved), then the angular velocity (rotational speed) of the skater must increase. read more