Well, I once had a non-lucid dream in which I was a giant fat goose sitting in the middle of a golf field, and I remember that I was pretty convinced that I was indeed a goose. Couldn't do much in that dream because I was too fat to fly or even waddle. I later interpretted this dream as my mind telling me that I am a silly goose.

While all my lucid dreams that I can remember either I had a human body or I couldn't feel a body at all, but I have read lots of lucid dream accounts of people with nonhuman bodies in lucid dreams. For example, I read an account of someone while in the lucid dream transformed himself into a leopard, and as far as I could tell from his description, it was a pretty awesome experience.

As for whether one can feel something that one has not felt before, do you mean like for example flying in dream and it feeling realistic? Yes, absolutely - well. at least as realistic as I can imagine it would feel to fly, given that in waking life I have no experience with flying, but dream flying is awesome, and feels as real as I can imagine - imagination and expectations are the limits here, and if those are not limited, there are no limits.