Simple. West Berlin was just a much better place to live in for the majority of the populace than East Berlin was, just as the Western Bloc was far superior to the Eastern Bloc.

1. Because West Berlin offered a much better quality of life, as even the Soviets admitted to themselves privately. You couldn't hide it behind propaganda as well in Berlin as in other places, with the West being just a couple of subway stops away before the Wall. If East Germany could offer a plausible reason for much of the populace to stay on their own merits, the Berlin Wall would not have been needed.

Who "used nukes" was completely irrelevant.

2. No, they were German. But Communist. East Germany was a fully functioning part of the Eastern Bloc, with its own government, armed forces, and secret police. To understand the GDR, it's best to think of East Germany as a Communist version of old-style Prussia (an irony of history was that the GDR was far more comfortable in some ways with Prussian military traditions than the West was, helped by the fact that they didn't do the collective guilt thing) with progressive slogans and the Party in place of the monarchy and the Junkers rather than a clone of the Soviet Union. It had its own culture. In fact, the mechanical, efficient, ruthless quality of East German socialism, not to mention the reputation of the NVA and the Stasi, gave them something of a creepy reputation even with their own allies in the Warsaw Pact. I remember reading a fiction novel about a Red Army veteran commenting on the difference between how the Germans and Russians implemented socialism: how even in defeat they did things "better", and how the mechanical quality of East German socialism might have meant a quicker life span for it in the end.

So there were some people who did buy into the regime-if there weren't, there wouldn't have been a Party or a government. It was their job to stop people going to the West, and they did their job.

1. People were fleeing because they did not want to be shut in the East with the political system and living conditions there, or because they had been separated from family in the West. Who "used nukes" on people halfway across the globe wasn't a consideration in that, particularly for anyone who understood how the Second World War had come to pass and who were the original "bad guys".

2. At the time the movie is set, both East and West Germany were autonomous states with their own government, police, and so on. While both had a military presence of the former occupying forces (now technically "allies"), the border was guarded by their own forces.

And as leaving East Germany was illegal, the border guards would have been in violation of their orders if they had helped people across. In fact, over the years a number of East German citizens were shot by East German guards when trying to cross the border. West German guards did not try to prevent them from crossing, but to reach the West German side, they'd first need to get past the guards and safety installations in the East.

While the guards in the East were German, they were part of a hierarchy, made to follow orders, and politically indoctrinated. Helping people over the border would have had severe consequences for them.