The Ringbearers in Aman & the fëar of Hobbits

Are there any theories of what would become of the mortals Frodo, Bilbo and Sam once they reach the undying lands? As far as I know, no mortal before them has been allowed to live amongst the elves and ainur in Aman. Connected to this: is anything know about the fëar of Hobbits? Are they "men" in that way, or rather like the Dwarves or Ents? Is anything known about this?