"It is interesting at university" was marked wrong because "you need the article "a" here" - it says I should have written "it is interesting at the university". To my ear this sounds far more unnatural than simply "at university". You certainly don't need an article there for it to make sense.
Agreed. "It is interesting at university" is a better/more natural answer. ("It is interesting at the university" should also be accepted.)
And most likely without "the" (unless you are talking about a specific campus).
It puts the emphasis on a different part of the sentence. The way you say it implies "the UNIVERSITY is interesting", whereas the sentence here would imply "it's INTERESTING at the university". I don't know if this is the same in Russian, however.
As a native english speaker, and an academic, saying "university is interesting" is perfectly fine.
'At university' means there for the purpose of study. 'At the university' means there for a different purpose, e.g. 'we went to the university to take a look around'