Displaying part of every child page?

Two suggestions:

  1. To output your “Loop” only for Child Pages, and not for Grandchild etc. Pages, add a conditional.

e.g.

foreach ( $mypages as $page ) {
     if ( $page->post_parent == $post->ID ) {
          // Loop goes here
     }
}
  1. To output only an excerpt of each Child Page, enable excerpt support for Pages, and then output $page->post_excerpt.

In functions.php:

add_post_type_support('page', 'excerpt');

Then in your “Loop”:

foreach ( $mypages as $page ) {

     if ( $page->post_parent == $post->ID ) {

              $content = $page->post_excerpt; // changed post_content to post_excerpt

              if( ! $content ) // Check for empty page
                   continue;

              $content = apply_filters( 'the_content', $content );
              ?>
              <h2><a href="https://wordpress.stackexchange.com/questions/16791/<?php echo get_page_link( $page->ID ) ?>"><?php echo $page->post_title ?></a></h2>
              <div class="entry"><?php echo $content ?></div>
              <?php

     }
}