If you have the motor out already, just make sure it is clear of the plastic teeth and reinstall it. Then take your new mast and with the help of another person you can install it from the outside.
They usually come with instructions, but the short gist of the matter is that you turn the key on and wait until the motor stops then feed the mast in with the teeth facing the rear of the car. Then the key is turned off and the motor will pull the mast in as it retracts.
To try and answer your other questions............the aluminum antenna has a tail of plastic teeth attached to the end that is manipulated by the motor to raise and lower the antenna. Most causes of failure are the breaking of the plastic "tail" inside the motor.
A replacement will include the antenna with the attached tail of teeth.
The actual radio connection is made to the motor housing, which I am sure you found out when you removed the motor.
