Short answers, pulled from the story.
The State of Vietnam was a Southeast Asian state that existed from 1949 to 1955, first as an associated state within the French Union and later as a fully independent state from June 1954. It claimed authority over all of Vietnam but controlled primarily delta regions and urban centers, while the communist-led Democratic Republic of Vietnam held roughly sixty percent of the territory by 1952.
Former emperor Bảo Đại served as Chief of State of the State of Vietnam from the 14th of June 1949 until he was ousted in 1955. He appointed Ngô Đình Diệm as Prime Minister in June 1954, and Diệm went on to win a fraudulent referendum and proclaim the Republic of Vietnam on the 26th of October 1955.
The Geneva Accords were signed between France and the Viet Minh on the 21st of July 1954, ending the First Indochina War by dividing Vietnam at the 17th parallel. The State of Vietnam and the United States rejected the settlement; Prime Minister Diệm announced in July 1955 that South Vietnam would not participate in the elections specified in the accords, arguing the state had not signed them and was not bound by them.
The official result of the October 1955 referendum showed 98.2 percent of voters supporting Diệm, a figure condemned as fraudulent. The total votes cast exceeded the number of registered voters by over 380,000; in Saigon, only 450,000 voters were registered but 605,025 votes were attributed to Diệm. Supporters of Bảo Đại were barred from campaigning and physically attacked.
Operation Passage to Freedom was a relocation effort during the 300-day period following the 1954 Geneva Accords. At least 500,000 Catholics, roughly 200,000 Buddhists, and tens of thousands from minority groups moved from north to south Vietnam via this operation, while around 120,000 Viet Minh personnel moved in the opposite direction.
The Domain of the Crown was an administrative unit of the State of Vietnam covering highland provinces where the Kinh ethnic group was not a majority. It was officially established on the 15th of April 1950 and comprised five provinces from the former Montagnard country of South Indochina as well as several autonomous territories in the north. It was dissolved on the 11th of March 1955.