The Berlin Airlift was in reaction to the Berlin Blockade. The United States and allies delivered supplies to West Berlin.
The Berlin Wall was to prevent all citizens of East Germany from escaping East Germany by going to West Berlin. It was built in 1961, long after the Holocaust, and had nothing to do with any distinction between Jews or Non-Jews, but rather East German citizens and West German citizens.
The citizens of West Berlin were moving to East Berlin, taking jobs away from the East Germans.
It was build in East Berlin, by the East German government (presumably at the behest of the Soviet Union), on the East Geman side of the border between East and West Berlin. Its purpose was to prevent the escape of East German citizens to West Berlin.
Parts of it, but most of it was torn down by West Berlin excavation companies who had the machines needed to do it right.
The Berlin Wall was the division between West Berlin and East Germany. The East German government built it to prevent its citizens from going to the West.
To prevent the citizens of East Berlin, which was under Communist Russian rule, from escaping to West Berlin, which was under the rule of the British, French, and Americans.
Since 1990, East and West Berlin have been unified as Berlin, the capital of Germany. In 1989, the Berlin Wall, which separated East and West Berlin fell. On 3 October 1990, German reunification was concluded, therefore the two Berlins unified as well.
It depended on your nationality, which way you were crossing it, and if you got caught. As far as the West Berlin authorities were concerned, there was no restriction on crossing the border. Anybody could cross from West Berlin to the DDR (East Germany, which surrounded West Berlin) or back again, without restriction. The DDR authorities did not have restrictions on letting people in. Crossing from the DDR to West Berlin was different. Western citizens (West Berlin citizens, BRD citizens (West German) and others) could cross back to West Berlin without problems. DDR and other Eastern Block citizens were not allowed by the DDR government to leave the country without permission. If they were caught, they would be sent to prison for a number of years. There was also a high risk of being shot while trying to cross the border illegally. If you succeeded in reaching West Berlin, there was no penalty; but you could never return to the DDR, as you were a wanted criminal.
American, French and British people airlifted food and supplies to the people of West Berlin whom faced starvation after Stalin cut it off.
The "Anti-Fascist Protection Wall" as the East Germans officially called it, was meant to prevent citizens of East Germany from going to West Berlin. West Berlin was controlled by the USA, France, and UK, and the East German government did not want its people going there.
West Berlin became prosperous while East Berlin struggled with communist pigheadedness and incompetence. Nobody tried to escape from West Berlin to East Berlin.