One type of tail rotor emergency in a helicopter is a total loss of tail rotor due to a mechanical failure. This could be a broken shaft, flex coupler, gearbox, etc. When this happens in hover flight, the helicopter will begin to spin out of control in the same direction that the main rotor system turns. The pilot will need to get rid of all main rotor torque by chopping the throttle and cushioning the landing (hover auto).
If this emergency happens during cruise, you will still need to enter an auto rotation. The difference in cruise flight is that you can fly far enough to spot a safe "spot" by keeping enough forward speed for the helicopter to weather vane. The helicopter will fly with a yaw until you are in the auto rotation. The auto rotation will have to be "full down" with no power recovery. Added power will cause the helicopter to spin out of control. It is important to only prolong the auto rotation a very short time. The failure that has occurred could be taking helicopter parts away, including the tail boom. If a helicopter loses too much weight, the center of gravity could be changed so much that it can not be landed safely with an auto rotation.
A helicopter examiner that I use has told me that some student pilots have told him that they are going to land a helicopter with loss of tail rotor thrust by sliding it on and controlling the heading with the throttle (This is a stuck pedal landing). This will not work for loss of tail rotor thrust and could cause you to fail the check ride.
Do not confuse the handling of this emergency with that of a stuck pedal. Stuck pedal=slide on / Loss of thrust=auto rotation.
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In your 3rd sentence the wording is incorrect. The helicopter will rotate opposite the main rotor with a loss of tail rotor thrust.