Rewrite slug for Custom Post Type?

Hello,
I have registered a custom post type called “books”, which supports categories and tags. In order to show the category in the permalink a rewrite array is created in my CPT: rewrite' => array('slug' => 'books/%category%.

Now, in order to get the correct category, the following rewrite code is written in my functions.php:

//Get category
add_filter('post_type_link', 'custom_permalink_structure', 10, 4);
function custom_permalink_structure($post_link, $post, $leavename, $sample) {
    if ( false !== strpos( $post_link, '%category%' ) ) {
        $glossary_letter = get_the_terms( $post->ID, 'category' );

        // adding check and reset
        if ( !$glossary_letter ) { $glossary_letter = array(); }
        // continue as you were

        $post_link = str_replace( '%category%', array_pop( $glossary_letter )->slug, $post_link );
    }
return $post_link;
}
//**End

This all works correct, but three things go not as desired:
1: When i post a cpt only in a subcategory, i.e. genre/adventure, then the URL is generated as follows: domain.com/books/adventure/post-name. However the default WP structure would generate an URL as follows (which is desired): domain.com/books/genre/adventure/post-name.

2: When i post a CPT in a subcategory and in the concerning parent category, i.e. parent category “genre” and subcategory “adventure”, the URL is generated as follows: domain.com/books/adventure/post-name. Whereas the default WP structure (which is desired) would generate an URL as follows: domain.com/books/genre/post-name

3: When i go to the archive page of a CPT, the URL looks as follows: domain.com/books/%category%. This is of course logical, since the slug is built that way. However, is there a way to filter the %category% tag when no %category% is defined?

I hope that someone can help me out with this. Help is greatly appreciated!!
Thanks, Robbert