Short answers, pulled from the story.
South Vietnam, officially the Republic of Vietnam, existed from 1955 to 1975. It first gained international recognition in 1949 as the State of Vietnam within the French Union, and the republic was formally proclaimed on the 26th of October 1955. It ceased to exist when communist forces captured Saigon on the 30th of April 1975.
Ngô Đình Diệm was the first president of the Republic of Vietnam, declaring himself president on the 26th of October 1955. He came to power after a referendum widely regarded as fraudulent, in which he was credited with 98 percent of the vote. He was overthrown and killed in a CIA-backed coup on the 1st of November 1963.
North Vietnam launched the Ho Chi Minh Campaign in early 1975, capturing Ban Me Thuot and then Huế and Da Nang. By early April, communist forces had overrun approximately three-fifths of South Vietnam. A last stand at Xuân Lộc failed, President Thiệu resigned on the 21st of April and fled to Taiwan, and General Dương Văn Minh unconditionally surrendered on the 30th of April 1975.
Personalism was a political doctrine that Diệm adopted as the official ideology of the Republic of Vietnam, positioning it as a third way between Marxist collectivism and Western individualistic capitalism. Diệm used it to argue that Vietnamese people were too poor to exercise political freedom immediately, justifying short-term authoritarian rule as a prerequisite for eventual democracy.
At the time of the Paris Peace Accords in January 1973, the South Vietnamese military was counted as the fourth largest in the world, with approximately one and a half million troops in uniform. At the peak of fighting during the Tet Offensive in 1968, over one million South Vietnamese soldiers were in the field alongside 500,000 US troops and 100,000 soldiers from allied nations.
After Saigon fell on the 30th of April 1975, the Provisional Revolutionary Government of the Republic of South Vietnam became the nominal government of the South. On the 2nd of July 1976, North Vietnam and this provisional government merged to form the Socialist Republic of Vietnam, and Saigon was renamed Ho Chi Minh City.