I agree that "What happens with the universities" is a pretty awkward sentence in English. It make me think that we have to do something with them. Like when you're helping a friend clean up after a party and you say "What happens with the beer cans, are they going to be recycled?" That's the closest sort of instance of that sentence structure making sense that I can come up with.
You can think of it like in English - we don't say "what are happening with the universities". We're using a subject pronoun which is singular: "what is happening with the universities?". ¿Qué pasa? is basically what is happening? in English.
(Slightly technical grammar things coming up, that you probably aren't even aware of when you speak English - but you probably know the rules and what sounds right and wrong!)
What could be talking about a single thing (what event is happening today?) or several (what events are happening?), but if we don't explicitly throw the subject noun out there (event in this case) we just treat what as the subject pronoun, and it's singular.
I think ThrashtilDeath is asking why you would say 'what happens with the universities' instead of 'what happens at/in universities'. The answer sentence doesn't really make sense in English, and I'm struggling to even think of an edge case!
Is this the Spanish way of asking "what happens at university?" How would the meaning change if you used 'en', or does that not work in Spanish?
The way I see it, a somewhat more accurate translation of this sentence than the far-too-literal one provided by Duolingo, would be something along the lines of "what's wrong with the universities", as in what's the matter or what's going on with them. Similarly, Spanish people would say "¿qué pasa contigo?", which roughly means "what's wrong / what's the matter with you?".
The Spanish way of asking "what happens at university" is just what you might expect: "¿qué pasa en la universidad?".
Not in modern English - the simple present is used for repetition and routine, so "what goes on with the universities" implies a question about universities in general, how they operate, what kind of things usually happen there. "What is going on with the universities" emphasises the present, what's happening now, and implies something different or unusual is taking place.
("What goes on with the universities" sounds strange anyway, we'd usually say something like "what goes on at universities?")