what would would have happened in the if the following events in South Vietnam had been differant
1) the elections were held in North and South Vietnam in 1956
2) Ngo Diem had either survived the now 1963 coup and remained in power or at the least escaped to a third nation
3) the communist took over South Vietnam was reunited with the North while both Ho Chi Minh AND Mao were BOTH living and in good phyiscal and mental shape
*Trying to remember Vietnam War class from years ago*
If the elections were held, Ho Chi Minh would have won. He led them to independence from the French after all. There's a reason the U.S. scrapped the idea.
The U.S. backed the coup against Diem, so LBJ would probably just try again, unless the story leaks out to the media somehow as the next "Bay of Pigs". Diem's brother Ngo Dinh Nhu and his wife Madame Nhu were also extremely unpopular. Look up Madame Nhu quotes if you want to know why; there's a reason people called her the Dragon Lady.
Even if the U.S. doesn't make a second attempt on Diem, there's a good chance he will be overthrown anyway.
The North Vietnamese would have to win pretty early for Ho Chi Minh to still be alive for reunification, as he was born in 1890. Mao was a little younger, so if Ho Chi Minh lives, it's possible the two could interact. Although China supplied Vietnam, the relationship between the two countries would be chilly at best. Communist countries often hated each other, and Vietnam's strong sense of nationalism would make it suspicious of China. Remember that a major Vietnamese hero is Le Loi, who led a war of independence against China in the 15th century. Such paranoia would make perfect sense for Vietnam; in OTL, China attacked Vietnam in 1979 over Vietnam's overthrow of the Khmer Rouge.
I may not be right about everything here. Feel free to correct.