Was Gollum a Hobbit? How did he not die after Bilbo took the ring?
Gollum was a Stoor, which is a type of Hobbit. Gollum would not have called himself a Hobbit, as that is a regional name for the race.
His longevity is the influence of the Ring. Apparently, it extended Gollum's lifespan for an indefinite amount of time.
Sméagol had been a Stoorish hobbit whose people had lived along the banks of the River Anduin. He possessed the One Ring for so long (about 500 years) than I would guess that his life was bound up with it and he would not die a natural death while the Ring still existed, but would eventually have been transformed into Wraith--albeit a lesser one.