Hello There,
Thanks for updating in!
1.) To add the product short description, please add the following code in your child theme’s functions.php file
function x_woocommerce_shop_product_thumbnails_custom() {
  GLOBAL $product;
  $id     = get_the_ID();
  $thumb  = 'entry';
  $rating = ( function_exists( 'wc_get_rating_html' ) ) ? wc_get_rating_html( $product->get_average_rating() ) : $product->get_rating_html();
  woocommerce_show_product_sale_flash();
  echo '<div class="entry-featured">';
    echo '<a href="' . get_the_permalink() . '">';
      echo get_the_post_thumbnail( $id, $thumb );
      if ( ! empty( $rating ) ) {
        echo '<div class="star-rating-container aggregate">' . $rating . '</div>';
      }
    echo '</a>';
if ( x_is_shop() )  woocommerce_template_single_excerpt();
  echo "</div>";
}
add_action('init', 'x_override_product_item', 99999999 );
function x_override_product_item () {
remove_action( 'woocommerce_before_shop_loop_item_title', 'x_woocommerce_shop_product_thumbnails', 10 );
add_action( 'woocommerce_before_shop_loop_item_title', 'x_woocommerce_shop_product_thumbnails_custom', 10 );
}
2.) You cannot add a custom text above the shop page contents. You cannot edit the Shop page using Cornerstone. If you want to add a Shop page description, you have to edit the shop page using the default WordPress editor.
          
             
          
And it will display above the shop columns:
          
             
          
3.) To manage the product sorting, please check this out:
4.) To display the short product descriptions needs to add the code given in #1.
Hope this helps. Please let us know how it goes.