An eye is Sauron's symbol because it representations his ever watchful gaze on Middle-earth
In the books he had a body, in one of Tolkien's letters he described him as taller then a man but not gigantic and that he should be thought of as quite terrible. He lost his ability to take on a 'fair form' when he drowned in the Fall of Numenor. He was also able to shape shift into a wolf, vampire, serpent etc (at least in the first age, we don't have any additional information about his shape shifting abilities in the third apart from what I already mentioned iirc)
I hope this is helpful in some way to you!! :D