>How does free college work in Poland?
Probably the same way it works in baltic states, you either get budget place if you have high scores, or, at the very least, you maintain said place while having good scores and no debts.
Probably, the free option is only about full-time study. No distance or part-time.
>Would I be able to get a free STEM degree?
Yes, granted that you study successfully.
>Could I get multiple degrees without having to pay?
Ehhh probably, but I would check just in case.
>Would I need a high level of fluency in Polish to get a degree?
In countries like Poland, free education is the one conducted in country's official language. English studies tend to be a premium option.
Also, chances are your teachers will be terrible in English or their curriculum is not as vigorous/more basic than the one in the main program.