@Svenja,
Hmm. You are going to have your work cut out for you but it's not impossible.
Of course everyone has school in common, and some have their fields of study in common as well. But it gets dull to just talk about Chemistry lab (or whatever), and in any event you can run out of what to say rather quickly. Then there's Politics and things like that, but it can get contentious, plus not everyone wants to discuss such things.
I wonder if some sort of a questions game would be useful. Maybe something like, you could ask people to form a circle. Then have them turn to the person to their left and guess what that person's greatest achievement is. Then that person tells them how close they got. It could turn out to be very funny or very accurate.
Since it's a positive question, I think people wouldn't mind giving answers. Or you could word it like,
what do you think ___ is famous for? And you might guess that I'm famous for making cherry pies (which I'm not). I might guess that you're famous for reciting the alphabet backwards.
I'll continue thinking about this. I think the last time I had to do something like this, I was rather young so it's been a while.