While this is a pretty big question to cram into an answer, I will try and cover some of it.

First question: The Nazis after World War 2 had a lot of different things happen. The focus was mainly on identifying high ranking Nazis and capturing them to face trial in what would be the Nuremberg trials. Herman Goring, Albert Speer , Himmler, and many other high ranking officials were brought into custody. The nazi scientists were granted immunity in many cases to spill secrets to the Americans and Russians in regards to nuclear technology, jet engines , and other technology. The rank and file either slipped through the cracks or if they were POWs by that time they were put into compulsory labor after the war. 1946 is when the US released most of the POW population to France and the UK. They then used them to clear minefields for the large part and the Soviet Union subjected them to a variety of very arduous forced labor (resulting in many deaths).

Next, roughly 375,000 ‘Germans’ migrated to the USA following the end of World War 2. Some more migrated in the 50s as well, it’s hard to say exactly how many soldiers were in that number but it is well known there were ‘thousands’ of Nazi conspirators and collaborators living in the USA following WW2.

Anyone could’ve escaped. The heat was mostly on the high ranking Nazis, some were captured and some escaped. The two notable ones , among many more were Adolf Eichmann (helped devise the Holocaust) and Josef Mengle (angel of death at Auschwitz).

There was sympathy for the Nazis in South America. Many of the leaders down in South America were sympathetic to Nazis and provided a safe haven to live their life. The Catholic Church and Red Cross provided many false passports for Nazis to escape through the rat lines of Europe post war.

To add on to the previous answer: the vast majority of them stayed in Germany, resumed their careers, and underwent "denazification."

The purpose of denazification was to keep former Nazis from occupying positions of power, and to restore German culture, society, and government. Unfortunately, no guidelines were written, and there were four different zones of occupation where there were four different ways of applying the program. Identifying former Nazis was mostly done by having people fill out questionaires about their roles in Nazi Germany, and in each zone, the answers meant different things. In the French zone, for example, not much distinction was made between "German" and "Nazi," and the waters were further muddied by relationships built during the Vichy regime. Most of the teachers were fired from their positions but rehired almost immediately because teachers were needed. The French also identified only thirteen of their prisoners as "major offenders." In the British zone, economic reconstruction was the primary goal, and the only people who had to answer whether they had been more than "nominal" Nazis were those who wanted positions of authority. The Soviets used their zone to build a Communist state; they imprisoned a great many people (including, famously, as much of the Polish Home Army as they could identify) and expropriated companies, factories, and farms. In the American zone, the questionnaires were taken seriously, but there was an enormous backlog and growing pressure at home for soldiers to return from Europe, so the legal aspects were turned over to the new German government in January 1946. Meanwhile, the U.S. Army tried to denazify the zone by tight control of media and censoring certain materials.

There were lots of Nazis who escaped notice and prosecution by buying documents saying they were not involved in the Nazi party; many of them escaped or were simply let go because the bureaucracy couldn't handle the volume of cases. Otmar Freiherr von Verschuer, for example, was a prominent genetics researcher until his death in 1969 in a car accident. Before and during the war, he ran the Department for Racial Hygiene as a eugenics researcher and carried out research using data he received from the work of his student, Dr. Josef Mengele, at Auschwitz. Mostly these people stayed in Germany or emigrated to the U.S. without even the smallest fear that they would stand trial, because the Allies were splintering with distinct post-war goals.