Hi,
I spent a lot of time on your website until I find that there is no issues in our code.
The page:
www.shemeck.pl/produkty/category/265-wyszukaj-wszystkie
is using a module to display the products.
But it should not, the products should be displayed by the menu as in any other categories.
So this module has issues in pagination with filter because it is a module inside a menu, this module should not have any pagination, so it is already a good point that the pagination is working and filters too , but combine the two will require custom code as it is not made for that.
May I ask why you are using this module and not displaying the products thanks to the menu as any other categories ?
If it is just to have a different layout than the other listings, you can potentially edit the view "product / listing_list" and thanks to a if condition based on the category id display one layout or another one.