Hi Lasindu:

You might consider doing your outputs in default.php a bit differently, mainly for code style / readability.

Instead of:

 <?php
   if ($position_attribute == "1") {
            echo $dataContact->con_position;
            ?><br>
                <?php
            }
?>

Consider this alternative:

<?php if ($position_attribute == "1") : ?>
<?php echo $dataContact->con_position; ?>
<br>
<?php endif; ?>

The reason is, because this allows you to then add HTML around the PHP elements a bit easier. For example:

<?php if ($position_attribute == "1") : ?>
   <div class="readon">
      <?php echo $dataContact->con_position; ?>
      <br>
   </div>
<?php endif; ?>

You'll find in Joomla when we do view outputting this is a fairly common method of writing if-statements in views.

https://github.com/lasinducharith/joomla-contactInfo-module/blob/master/tmpl/default.php#L51

The text 'Email" should use JText so it can be translated into other languages :)

Out of preference I'd rather just show the email address like you had in the photo in the GSOC (something like
echo JHtml::_('email.cloak', $dataContact->email_to);
but thats just my personal preference and is up to you (although you could always have it as a parameter)

I'd like to see you use more of jdatabasequery in your query. That is separate it out into

$query->select('')

and so on, using chaining. For this query id doesn't matter so much but for more complex ones it will. Plus always use $db->quote() and $db->quoteName() where appropriate.

Nice job!

Also think about making country optional in the address block.