The biggest problem of goods transport was actually during the Berlin blockade in '48 and '49, the Soviet Union closed all land based access to Berlin forcing the western powers to organize supply through airlifting the goods into Berlin Tempelhof airport (the airport is now a city park). Besides air traffic road and rail traffic was possible on limited routes, but west German citizens traveling through east Germany required permits. As for the wall: it did indeed enclose the entirety of West Berlin.

Some of the guard towers of the DDR are still standing, traveling on the A2 you will see quite a few as this was the major highway westwards. Also the old border checkpoint on that highway still exists and is now a monument