In English, "Soviet" is the adjectival form of "USSR".

Because Soviets are a central part of how the USSR was organised.

And in 1968, did they believe that this was how things were done in the USSR?

Copying on things were in the USSR wasn't the point. The point are certain Marxist ideas about the value of Soviets for political organisation.

What is the actual structure at the Free University of Berlin (FU) that you're referring to?

A system of of soviets, as I said above. There a lot of ideas involved. On the left you had a split between people who believe in social democracy and people who are Marxists. The FU Asta is Marxist.

The people sitting in it are still Marxist even through the majority of the student population of the FU isn't and they don't have a problem with that as they don't believe in representative democracy. They also defend their right to use their printing press to print whatever they want by not disclosing what they are printing. By law they are only allowed to print for university purposes and not for general political activism.