They learn the theory behind algorithms, data structures, and computation in general. Anything a computer can do (and some things they can't) fit within the field of study.

what is capable to do a compter scientist?

Beautiful women.

do they make their own library?

Yes.

or they work with one that already exists?

Yes.

btw I havent started university yet so I want to apply maths stuff into a basic 2d game for example

That's just fine.

To quote what we were told A LOT at university: computer scientists are NOT programmers (in fact, some people couldn't have coded their way out of a paper bag and still finished with decent grades.. in the theoretical and technical branches)

computer scientists are NOT programmers (in fact, some people couldn't have coded their way out of a paper bag and still finished with decent grades.. in the theoretical and technical branches)

The same was true when I did 'software engineering' at university

To quote what we were told A LOT at university: computer scientists are NOT programmers (in fact, some people couldn't have coded their way out of a paper bag and still finished with decent grades.. in the theoretical and technical branches)

QFT.

If you want to be a programmer, you will learn faster and better on your own that a CS program will teach you (CS programs don't teach programming, it's just an incidental skill you have to pick up).

Yes, "Computer Science" means that you're doing science with computers (or, put another way, using computers to do science). Programming languages are just a useful tool to getting computers to do what you need them to do. With that in mind, a good computer scientist has a background in science and mathematics.

...but, since this is a game programming site, I imagine that you're trying to pick up the necessary skills to make games. If you're going to be a game programmer, programming is absolutely necessary. A solid understanding of datastructures and algorithms will be your bread and butter. My personal recommendation is to just start teaching yourself by using online tutorials and references to make simple games and use the university education to supplement your existing knowledge and experience. The classes you'll take will have much more meaning for you when you have something to put it into context with.