Your cat sounds very very happy and affectionate! If your cat is biting you hard, you may want to read more about why your cat is biting you.
Cats are usually very very happy when they are purring. However, a veterinarian once told me that biting is not an affectionate behavior in cats. I’m not so sure I agree with her. One of my cats will often start purring very loudly. If I continue to pet him, he will usually bite my skin very lightly.
When cats bite while they are purring, it usually seems like a love bite to me. I like to tell myself that anyways 🙂