1) Why is "at university" wrong? Does this word always be followed by "a" or "the"? Thank you.
2) Can you help me express this?
You found it difficult to express your personal opinions as well as to revise your topics critically.
I'd need to see a whole sentence with "at university" in it to tell. Generally, I'd take it that "at university" means that someone is going school at some unnamed university, but "at the university" means that both the speaker and the listener know exactly which university is being referred to.
He is going to university next fall. (Same as this: He is going to college next fall.)
He is going to the university next fall. (means that both the speaker and the listener know which specific university is referred to)
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I don't find any problem with the sentence you posted. Do you need to revise using synonyms or something?