How do I make it so that new posts within a certain category go into a certain page?

You mean you want to make a page and show posts of your fashion category in it?

Sure, it’s easy. Assuming that the ID of your fashion category is 123, you can try this:

    $args = array(
        'posts_per_page' => 10, 
        'cat' => '123',
    );

    $fashion_query = new WP_Query($args);
    if ( $fashion_query->have_posts() ) {
        while ( $fashion_query->have_posts() ) : the_post();
            the_content();
        endwhile;
    }
    wp_reset_query();

Make a PHP file of a page you like, then copy the code above wherever you want in your page template.