It isn't so much a plural as a collective noun - it turns the noun into 'group including the noun', which doesn't have to be all the same type of thing (like, if they're mostly university students but there's one high schooler with them, you can still use 大学生たちto refer to the group).
It only need to have two colleges/schools to be considered a university. Also, there are universities that only offer undergraduate degrees. I went to a university that had two schools, one for liberal arts and one for business, and was only a four-year undergraduate institution. The schools are part of the same campus and community, I think the only seperation was were some of the funding came from. A liberal arts student could take business courses and vice versa.
It's highly context specific as well as country specific. In the UK some educational institutions for children up to 18 are called "colleges" in their name (for historical reasons); many separate educational institutions specialising in 16-18 education are called "colleges" by those attending them (they are often known as "sixth form colleges" - the sixth form being the last two years of school).
But college is sometimes used for higher and/or further education (i.e. education beyond the years of compulsory school-age education - I am using "school" in the UK sense, rather than the looser US sense). "I went to college" or "I am going to college" could mean a teenager taking her A-levels, but it could also mean someone taking a degree or even higher degree such as a master's.
Having said all that, "college" is also a term for subdivisions of several universities. For historical reasons in the case of Oxford and Cambridge, where the colleges are separate legal entities from the university and responsibility for teaching is primarily on the college though farmed out to the university. Other more modern universities have copied this model, though sometimes here the "colleges" are not separate legal entities.
"College" is of course a more general word and in some contexts indicates other groups. Eg the "college of cardinals" who elect the Pope. In the Church of England a cathedral will have a number of associated individuals known as "canons" who are collectively the "college of canons".
In short: in the UK "college" doesn't provide sufficient information without context.
It varies depending on the country. In the USA, "college" refers to an institution which only offers undergraduate degrees (e.g. the undergrad portion of Harvard is 'Harvard College', which is under the 'Harvard University' umbrella), but they largely interchangeable in the US (e.g. when applying for post-secondary education, we always say that we're completing "college applications", not "university applications"). On the other hand, in Canada, college refers to vocational, trade, or diploma school and university is an institution offering bachelor's, master's, PhD, MD, DMD, DVM, etc. programs, but "college" can also refer to an institution within a university (e.g. the University of Toronto has 7 colleges for undergraduate arts and science students).
In the US, "college" is generally interchangeable with "university". Whether you attend a college or a university, you would say "I'm in college" (e.g. "I'm a college student at the University of "). But to be more technical, the difference between a college and a university is the highest level of degree they grant. A college only provides bachelors degrees (4 years) whereas a university provides masters (+2 years) and PhDs (+~5 years).
The reason we don't use "university school" (from what I know about English anyways) is because the words elementary, middle and high are used as adjectives to differentiate the schools. If you say "I am going to school" it could be an elementary school, a middle school or high school that you're going to. However, university is never used as an adjective, so we can't use it here to differentiate a university and, say, a high school. That's why we use university and not university school. Hope this cleared things up for you :)
Thanks for the answer.
I agree, but "student" means either "pupil" or "college student". Therefore "student" shouldn't be wrong. I'm not a native speaker though. All I can say is that when I look up the german word "Student", which means "college student", the dictionary of my choice tells me "student (at university)".
I understand that it's perhaps different in German. In Japanese, "student" translates to "学生" ("a life of study") and indicates anyone, of any age or level, learning at an educational institution. Therefore, the 大~ is a specifier that should carry over in the English translation as well.