His actual name is not Slimer. No one knows his real name or who he was before he died. Nor does anyone know how he died. His missing legs may be a clue. Perhaps they were blown off in combat and he bled to death. Or maybe he just never had legs. Whatever the circumstances of his passing, something kept him here on Earth. Possibly his search for his missing legs.
It makes no sense that he would eat. As a ghost, his physical manifestation has no way to metabolize the food he consumes. My guess is that it’s an emotional based eating, possibly a cry for help.