There's a lot of difference between american and our school system, and the terminology can also be confusing.
Pre-school is zabavište (zabavljati - to entertain; zabavilja is thus a teacher there). One year, at age 6, can do at 5 if a psychologist agrees or recommends.
Elementary school covers grades 1 to 8.
Middle school - grades 1 to 4, corresponds to american high school. gimnazija, MPSŠC, 13. are middle schools. In the times between 1979 and throughout the eighties, we had šuvarice, after the croatian politician and school reformer Stipe Šuvar, whereby the 1-2 grades were considered an extension of elementary, with the idea that even vocational schools would have the general education, actually the kids would be mixed at random, no elite schools until age of 16, then 3rd grade would be all vocational (degree of qualified worker), and 4th would be optional (technician). This almost worked, but was riddled with its own paradoxes and landed on the unfertile soil - nobody liked it, specially not those who were supposed to make it work. So a decade was lost, and then it got worse.
University is an university, but it consists of
- higher schools, i.e. half-colleges, two year, where one gets some lesser title, "plant engineer" or just economist etc, without the "dipl." prefix. The „plant“ prefix was dropped after around 2001, because of deindustrialization, now it's „strukovni“, where „struka“ means the discipline, branch of knowledge, vocation, area of expertise, all in one.
- fakultet - which is the same word as faculty but means college here. What's faculty here is called kolegijum. There you go.
Also, when one says student, that's university student. Anything below is učenik - literally a learner, a disciple, a pupil.
On the staff side, there are teachers - for elementary, grades 1 to 4. Below that, vaspitač(ica, suffix for female) - upbringer. Grades 5 to 8, nastavnik (lecturer... roughly, though lecturer is rather a predavač; perhaps it meant something else in russian original). Middle school and higher education, professor.
To be a teacher, one had to finish the teacher's middle school, until the seventies, then the law changed and they have to have at least a higher school now. For lecturers, a higher school was always required (as far early on as I know), don't know if that was raised (it was, in the seventies - both Jablan and Lazar were taking extra courses at the time). For middle school professor, a fakultet diploma. Above that, the usual academic degrees - asistent, docent, vanredni profesor (extraordinaire), redovni profesor (tenured, i.e. regular). At some point in there a doctorate is required.
Grades, i.e. marks: for elementary and middle: 1 - insufficient (i.e. fail), 2 - sufficient (i.e. pass), 3 - good, 4 - very good, 5 - excellent, except in case of conduct, where 5 is described as exemplary. Fun fact: word for conduct is „vladanje“, which primarily means „ruling“ (i.e. being in power, authority, governing) and then „behaving oneself“. In higher education the range is theoretically 1 to 10, where the lower half means fail. The fail marks are not written into student's index (booklet which serves as both an ID and a cumulative academic record), except when a professor is in a specially bad mood. Everyone knows someone who heard of a story where it actually happened. Likewise, just about ten times les frequent, is that there may be a professor who would fail a student with a mark below 5 - including a once-in-a-century story of a zero. Such tales are a matter of academic folklore, though.
To pass into next grade it is generally required to pass each subject. At elementary and middle level, up to two fails are allowed for the remedial exam, which is held twice - by the end of june and end of august. Anyone with more than two aces (1 marks) fails the year; anyone who doesn't pass the exams after these two retries, also fails. Now this somehow contradicts the law which said the elementary school is mandatory - so if it's mandatory and you can fail the grades... how then? They'd usually keep one in for up to two extra years, and then they'd be 17 and just too old to be in the same class with those of 14-15 years of age.
However, some politicians had the bright idea, some time in mid-seventies, to abolish the failed in elementary, which then created generations of those who were content to do absolutely nothing, knowing that they have a free pass. Then they entered the middle school system, which has both the "you can fail the year" and "this is not mandatory, we can kick you out", but then the time in there was too short to develop any kind of attitude change. They still expected a free pass.