East Germany will be GDR (German Democratic Republic) and West Germany will be FRG (Federal Republic of Germany.)

It was indeed possible for an East German to leave the GDR, the only issues being how difficult it was to acquire the passport and permission to visit (yes, they needed permission.) In order for to get the passport and permission, you would need an extensive background check (they didn’t want anyone showing signs of wanting to defect to get to the west) and pay large fees (this deterred people from applying.) Because the regulations of the GDR changed over time, I’ll be answering the question by the time eras.

Upon the initial separation of Germany (starting in 1945 with the Allied Occupied Germany) up until the 13th of August 1961, border crossing was, at least in East Berlin, incredibly easy. It took nothing more than a simple walk, drive, or bicycle ride to reach West Berlin. During this time 3.5 million people (over 20% of the GDR population) defected to the FRG, most of whom went through Berlin. Just about all of this was illegal, with some very rare exceptions. The GDR couldn’t do anything about it, so they took full measures to stop this and began building the Berlin Wall in August 1961.

Following the 13th of August 1961 (construction of the wall started), most forms of legal and illegal border crossing stopped. Not just for people intending to live in West Berlin, but even visits came to an abrupt halt. The only people that could visit were retired citizens (those not contributing to the GDR economy) and the very few people that were deemed eligible to visit.

In 1971 a GDR politician called Erich Honecker came to power. One year later, in 1972, he began making it possible for working citizens to visit the West. It was still difficult, but nonetheless easier than before.

In the late 80’s there were protests for greater freedom of travel in the GDR. On the 9th of November 1989 there was an announcement made on television that freedom of travel would be implemented across the GDR. It was planned to take place the following day, but the date wasn’t placed on the paper of the person announcing this, so he said that it was to come into effect immediately. This started a frenzy with the East Berliners, they ran to the wall in masses. The border guards couldn’t do anything, so they let the citizens pass by and thus began the demolition of the Berlin Wall. From that date forward there was no restriction of travel on East Germans.

To answer your question about the international airport, the GDR airlines (Interflug) travelled to a very limited number of cities (all of which were in socialist nations, the FRG, or in neutral nations like Austria and Cyprus.) The airport also would have been used to import from foreign nations.

This isn’t a sponsor or anything, but I recommend reading Forty Autumns: A Family's Story of Courage and Survival on Both Sides of the Berlin Wall. It’s a non fictional book based on a family that got separated by the Iron Curtain and very well describes the situation at the time. That’s where I got most of my answers from. Another source was the Ted Ed video about the Berlin Wall (this is an excellent place to start learning about the Berlin Wall, it’s where I started learning.)