How can hashes be unique if they are limited in number?
how can for example SHA-256 be unique if there is only a limited number of them?!


Where your issue occurs is that they're not unique.  It's just very improbable that they'll reoccur.      Unique in this context is not a mathematical definition, it's a humanist one.  

In terms of human numbers, $ 2^{256} $ = 115792089237316195423570985008687907853269984665640564039457584007913129639936 which is 0.1% of the number of atoms in the visible universe. So that's a lot of them.

There's a better  answer @ Why haven&#39;t any SHA-256 collisions been found yet?, but you should get the gist from the lengthy 116 quattuorvigintillion number.