No. His nose is the same as a serpent because he broke his soul into 7 pieces. (Horcruxes) It's shaped like a serpent because the serpent was the thing that tempted Adam and Eve. It wouldn't have helped at all if he got a nose job, he was still completely evil.
He had a nose at one point in his life. I'm sure after a certain point though, he stopped caring about his appearance and about what others thought of him.
yes, at least it would make him feel better somehow
i think so,