Can I get entries related to one category from a specific site?
Relations don't work with a slug. You'll need to insert an ElementQuery an Element or the ID of an Element

{% set entries = craft.entries
    .section('sectionHandle')
    .relatedTo(category)
    .site('siteHandle')
    .all() 
%}


However this will only work in certain cases where all category ids are the same for both sites. You'll need to to fetch the category from the other site at first if these are different