As far as I know - after consulting several different dictionaries - the word Studenter (sic) does not exist in the German language. There is, however, another word for 'a student': Studierende/r (mf). It is one of those pesky nouns that behave like adjectives, and since I have not quite figured out how that works, I do not dare to say anything more specific about how it is used.
It's the actual pronunciation that matters. The first sound in "university" /juːnɪˈvɜːsətiː/ is not a vowel. That's why you need to use "a".
True! If you're translating from Englisch to German that should've been acceptable, since in English the gender isn't given. It can be either eine Studentin or ein Student!
(But I just noticed; you need to translate "a" and "ein/eine" if needed. That's why the app says it's incorrect.)