Hi am new to learning helicopter flight and picked up the AXE CP. I read Rudd's instructions and am up to battery 3 and 4. I notice the tail rudder only spins when I apply move the right stick right. This makes following his steps pretty tough. I also noticed when I start applying more head spead the heli shakes like crazy. Any advice here would help.

That's normal. Tail motor helis use a fixed pitch tail rotor. On the Axe this means when you apply left rudder the tail motor decreases or on hard left rudder will stop completely. The heli relies on the torque of the main rotor to nose left.

Are your blades tracking correctly? If so it sounds like your rotorhead is out of balance. Even though the Axe it's supposed to come balanced and trimmed out it's not. You have to balance the blades and the rotorhead.