How JomSocial's avatar is updated is determined by you. There's a setting in the Profiles area of JFBConnect, when the JomSocial profile plugin is enabled, to import the users profile every time they login or just on registration. If you have this set to Yes, then when they login, their avatar will be updated, and the avatar in the JFBCLogin should always be the same as what's in their profile.
To add the link, try the following change in the /modules/mod_jfbclogin/tmpl/default.php file. At line 97, you'll see the code where the Facebook image is inserted <fb:profile-pic... Change this to:
<div id="profile-pic">
<?php $link = JRoute::_('index.php?option=com_community&view=profile'); ?>
<a href="<?php echo $link; ?>">
<fb:profile-pic uid="<?php echo $fbUid;?>"
size="<?php echo $params->get('picQuality'); ?>"
<?php echo $picHeight;?>
<?php echo $picWidth;?>
linked="<?php echo $linked;?>"
facebook-logo="<?php echo $fbLogo;?>"
/>
</a>
</div>
Let us know how that goes. You should just be able to cut and place that code and replace the div that's already in the module.
Good luck!