how to show this part only in the single post page?

You can use is_single() in a conditional statement.

<?php if( is_single() ){ ?>
  <ul>
    <li class="Source"><a>source:</a></li>
       <ul class="Source-Link">
           <li><a href="https://wordpress.stackexchange.com/questions/121060/<?php echo get_post_meta($post->ID,"source-link', true); ?>" target="_blank"><?php echo get_post_meta($post->ID, 'source', true); ?></a></li>
       </ul>
    </li>
  </ul>
<?php }?>

Be aware though that this will appear on any single page, meaning a single post page and a single page.

http://codex.wordpress.org/Function_Reference/is_singular