The aftermath of the fall of Saigon was a complicated situation for anyone tied to the old regime, to say the least. It also was not a good time for landowners, business owners, or the upper and middle classes. And furthermore, there was a period of time in which it was also not comfortable for the urban and rural poor as well.

Immediately after the fall, there were hundreds, if not thousands of extrajudicial killings that occured throughout the former South Vietnam. While this generally was not an organized plan on behalf of the new regime, we know that individual acts of personal and political retaliation occurred. This also generally was the end result for those ARVN soldiers who resolved to keep fighting beyond the ceasefire on April 30. One such example was Colonel Ho Ngoc Can, province chief of Chuong Thien Province, who elected to continue fighting. He was captured, and eventually executed in Can Tho stadium in August 1975. There are purported photos of his trial, but I have not been able to confirm this independently.

The Spring Offensive resulted in hundreds of thousands of internally displaced peoples flocking to the southernmost cities, particularly Saigon. However, the new regime had a plan in place to deal with this: New Economic Zones (NEZ). Under this plan, northerners were directed to move to the south, while southerners would be displaced and moved to remote, often mountainous areas, to establish new hamlets and communes and farm the land. These new agricultural operations would end up having much of the harvest seized and redistributed, as the forced collectivization of southern farms and complete disruption of the southern capitalist economy resulted in a major economic downturn and famine. The most prominent problem with the New Economic Zones is is that it involved the mass eviction of people from their homes, in addition to the seizure of land and businesses. Many of those who had their businesses seized were from the Hoa ethnic group. Additionally, the NEZ's were often far removed from urban areas, and featured no existing infrastructure. As a result, many died from sickness and starvation. Between 750,000 and 1 million people were forcibly relocated to the NEZ's, with approximately 50,000 dying in them.

One other aspect of post-war Vietnam were the Reeducation Camps. All government officials, most low-level government employees, bureaucrats, politicians who sat in the National Assembly, prominent religious officials (both Catholic and Buddhist, as well as other smaller sects), in some cases teachers and university professors, and former and active military personnel were required to report to camps. In a nutshell, the lower your rank or tenure was, the less time you were to spend in the camps, learning about socialist theory and "atoning" for one's role in perpetuating the war.

Those at the bottom of government or civil society, as well as those in the lowest ranks of the military were to pack enough belongings for up to one week, mid-level people were to bring enough clothes for a few weeks, and the highest officials were to prepare for up to a month. These men (and women) were told to bring some clothes and personel toiletries, but generally no other personal belongings. In addition to the forced indoctrination, the Reeducation Camps also doubled as hard labor camps, which involved jungle labor and mine clearing. They were located all over the country and generally in remote, jungle areas, which made escape incredibly difficult. Over 300,000 people were ordered to the camps. Although many were released in as little as a few weeks, many South Vietnamese military personnel, mostly mid- and senior-level officers, and some of the most prominent government officials would endure the camps for multiple years and in some cases, decades. The last South Vietnamese generals were released in the early 1990s. Although camp inmates were allowed visits by family on occasion (whereupon family members would bring extra food for inmates), in general little food or medicine was available in the camps, as everything had to be grown within the camps or harvested just outside while under guard. As a result, an estimated 165,000 died in the camps, buried in unmarked graves.

Furthermore, many South Vietnamese were unable to find work because of their previous government affiliations, and the economic disaster that was the collectivization of the South Vietnamese economy meant that many found themselves destitute and starving. As a result, millions chose to flee Vietnam, by either the risky overland route to Thailand, or to the sea lanes of the South China Sea. Mostly in old fishing boats, often overloaded by two, three, and four times the capacity, the boat people would bribe local government officials and coastal guards in order to leave. Families would generally pay for passage on these boats in gold—usually their entire life savings. Frequent attacks by pirates and coast guards who knew these refugees would be carrying valuables resulted in countless killings and sexual violence, and furthermore the old fishing boats were generally not equipped for deep ocean travel. Those lucky enough to drift into shipping lanes would be rescued by passing freighters or by US Navy ships. Many headed for Malaysia or Indonesia, where unfortunately, maritime patrols and coast guards would push them back out to sea. In the all of cases, they were interned in refugee camps for resettlement. Some would die in the camps while waiting to be granted asylum. UNHCR estimates approximately 400,000 boat people died, though we'll never have a solid number.

Now in terms of the change in governance, the Provisional Revolutionary Government (PRG), the political branch of the National Liberation Front (Viet Cong), officially took power in the south on April 30, 1975. However, the NLF had always been directed by the North Vietnamese Politburo, and many of the northern government did not trust southerners. As a result, officials of the PRG found themselves increasingly sidelined and driven out of their positions until July 2, 1976, when the PRG was officially dissolved to form the new Socialist Republic of Vietnam. For example, Trương Như Tảng, Minister of Justice for the PRG and a southerner, spent more than eight years in the jungle as part of the communist insurgency but eventually chose to flee Vietnam after being sidelined by the new government.

In summation, the days and years after the fall of Saigon were marked by political repression and economic turmoil. To more directly answer the second part of your question, the United States generally opposed formal diplomatic relations with the new Vietnamese government and in fact during its war with Cambodia, the US actually supported the Coalition Government of Democratic Kampuchea which including the Khmer Rouge. It was not until 1994 that the US would lift its trade embargo on Vietnam and normalize relations in 1995.

For further reading on the political and economic situation within southern Vietnam after the war, I recommend The Bamboo Gulag: Political Imprisonment in Communist Vietnam by Nghia M. Vo and Vietnam Under Communism, 1975-1982 by Nguyen Van Canh. Canh's book in particular examines the economic situation postwar which resulted in Vietnam's "Doi Moi" policy and shift towards a socialist market economy, instead of the Stalinism that led to economic ruin.