Fist error I see is a syntax error:
depth => 0
should be
"depth" => 0
Second error is that you are using a category object like a post object. None of these lines will work:
There is no post data to setup. Remove this line:
setup_postdata($category);
A category object has no category_modified property. Maybe you need the date of the last published post on the category (this is another question)???
//Not valid property
$category->category_modified;
get_permalink() is for posts, for categories use get_category_link() instead. Also, $category->ID is not a valid property of a category object, use $category->term_id instead:
//Incorrect
get_permalink($category->ID);
//Correct
get_category_link($category->term_id);