The original question had to be edited as only one question can be asked. The subsequent questions were interesting ones, and I would suggest resubmitting them. Nixon's plan to give ownership back to the Vietnamese was rooted in a couple of ideas. The first was that the war was growing in unpopularity. The rising casualty count, the lack of definable and tangible success, and the belief that the government was lying to its citizens all fueled resentment towards the war in Vietnam. Nixon understood that Vietnam all but finished off President Johnson because of its lack of definition. As he was elected into office under the "Peace with honor" notion, Nixon and his advisors figured that the Vietnamization was the best approach in which Nixon could say to the public that he ended the war and did so without the dreaded "cut and run" label.
In embracing Vietnamization, Nixon was able to make a compelling case to the American public that he was giving ownership of the war back to the Vietnamese. This became a very compelling point with the American public and justified why Nixon embraced it:
The key new element in our strategy was a plan for the complete withdrawal of all American combat forces from Vietnam. Americans needed tangible evidence that we were winding down the war, and the South Vietnamese needed to be given more responsibility for their defense .... As South Vietnamese forces became stronger, the rate of American withdrawal could become greater.
Vietnamization accomplished a couple of elements. The first was it forced the South Vietnamese government which had become accustomed to American forces bearng the brunt of the military action, to be more responsible in accepting the consequences of the conflict. At the same time, it was a way in which American military presence could be dialed down, pleasing the American public and honoring military obligations in the region. In this, one can see why Nixon sought to give ownership of the war back to the Vietnamese.