There were around 650 of us as freshmen, but the number plummeted over the past two years, the number plummeted to 350 or so.

This isn't super strict, I think it just sounds more natural this way.

Many of them ratherprefer to start working in the IT field even without a degree, whichas it is not usually required.

I'm a third year student of bachelor'sundergraduate student in computer science at Brno University of Technology.

This is a much more common way to say that!

Then they can choose to begin their study again as freshmen, in which case they may request that the university to accepts their passed courses, so they don't have to register for them again.

One is that people in the first year realized that the major they chose is not what they wanted or what they expected.

The other reason is that the university ends people's study when they don't meet conditions set by the university such as: acquireing enough credits during a semester, or pass aing a (certain) course.

I wouldn’t use a colon to set off a list unless the list has at least three items.

“A certain course makes more sense to me,” whereas “a course” potentially suggests “at least one course.” Alternatively, “passing their courses” would also be fine, but the meaning would obviously be different.

If a student fails it all three times, they must register for the course again the next year.

Then they can choose to begin their study again as freshmen, in which case they may request the university to accept their passed courses, so they don't have to register for them again.