It was possible to cross the Berlin Wall. I haven't seen Deutschland 83 so I can't refer specifically to it, but while the wall was a series of fortifications to prevent free movement, there was border crossings and ways to cross the wall legally. Of course, it was much easier to cross west to east, than east to west.

The Berlin Was built in 1961 and fell in Nov. 1989. The policies changed depending on the relations between East & West.

But East Germans might be allowed to cross into W. Berlin or further west for professional reasons such as conferences. If they remained in the West, any family left behind would suffer.

East Germany also from the 70s allowed retirees (over 65 years old) to freely move to West Germany. This was a form of social dumping of course.

Allied and USSR military personnel were allowed freely to cross as long as unarmed and in uniform. This was part of the post-war power sharing agreement.

In the early 60s East Germany had campaigns appealing to young West Germans to move to East Germany to escape the perceived growing authoritarianism of West Germany. It drew a few but not many. The legal age of marriage was also lower in East Germany, so there were couples who eloped into East Germany. There was also people in West Germany who moved to the East because they missed their families who they were separated from when the country was divided. There is only one confirmed death of a man killed attempting to cross the inner-German border from West to East.

It became a common practice for tourists to visit West Berlin and then get a day visa to visit East Berlin.

There is an interesting history of people who actually freely moved into the East. It was a one way ticket if they gave up their West German citizenship. There was plenty trade and interaction between both sides.

The problem is for those in the east wanting to travel to the west. That's something that was only allowed for a select few.