Let say there a rod pinned down tightly to the floor with no friction between the pin and rod. If a ball was to move at the same velocity and collide and stick together with the rod at some radius perpendicular to the position, would the linear momentum be converted all into angular momentum after the collision?
Both quantity have different dimension, you can cannot convert time into distance, now although there exist a relation between linear and angular momentum which is related to their velocity $v=wr$, you can use both angular momentum and linear momentum conservation in this problem. Or best you can use energy conservation which holds here.
Yes, it would. At the instant when the ball touches the rod, it coukd be thought of as having angular momentum in the form of mrv. It is intuitive to think it would make no difference if the ball was rotating around the center or following a tangent linear path if it would impact the same place at the same instantaneous speed. Thus, think of the ball in terms of its speed and distance from the center of rotation, and think of its mass as its moment of inertia given the center of rotation. Also, conservation of momentum is a corrolary of Newton's Third Law, so it will always hold.