So if it is possible he was the oldest living MAN and men only lived so many years, not many in the big picture would he have not had to have been half elven at one point in order to make a choice to stay a man and thus the long life.Or did Sauron have the ability to keep him living, and if so would that not negate his being a man, would he not have been diminished into a wraith type of being
This wasn't a choice or Iluvatar problem, this was an anomaly. The Mouth of Sauron was just a man and Sauron probably augmented his lifespan with some magics, but who calls that living. Anyway, he was only a minor bit player and Tolkien never gave him more than those few lines in the RotK and didn't have an inkling that we fans would be wasting our time worrying about the Mouth's biography. If he had, I'm sure he would have deleted a few words or added a few more in order to not keep us awake in the wee small hours worrying about this non-problem.