are all species immortal in valinor

[zifnab]

It says in The Return of the King, in Appendix B(Chronoloy of the Westlands), Later events concerning the memebers of the fellowship of the ring:

1482 Death of Mistress Rose, wife of Master Samwise rides out from Bag End. He comes to the Tower Hills, and is last seen by Elanor, to whom he gives the Red Book afterwards kept by the Fairbairns. Among them the tradition is handed down from Elanor that Samwise passed the Towers, and went to the Grey Havens, and passed over Sea, last of the Ring-Bearers.

1541 In this year on March 1st came at last the Passing of King Elessar. It is said that the beds of Meriadoc and Peregrin were set besides the bed of their great king. The legolas built a grey ship in Ithilien, and sailed down Anduin and so over Sea; and with him, it is said, went Gimli the Dwarf. And when that ship passed an end was come in Middle-Earth of the Fellowship of the Ring.

And yes Samwise was mayor for 7 terms.