We see the form of Sauron in the beginning of the first movie when he is beaten by Isildur and in the rest of the movies we see him as the eye. I think that in order to be in his true form again he must be reunited with the ring. The mouth of Sauron is just a messanger of him in order to negotiate with the Free people of Middle Earth... Is this correct?
The Mouth was just speaking for him. Think of him as Sauron's PR guy and diplomat. Sauron was like Gandalf and was a Maiar. Only few of them were created and dispatched to Middle Earth.
Mouth of Sauron is just a puppet who speaks and acts on Sauron's behalf. He's a separate being but is completely subservient to Sauron.
I am pretty sure Sauron actually is the pupil in the "eye" as can be seen during his confrontation with Gandalf in the second Hobbit movie. That's how I see it in the movies at least, I am pretty sure it's not that way in the books.
That's correct from what I understand. After Isildur defeated him, his spirit embodied itself in the "eye."
