The function you want is elgg_is_admin_logged_in()

http://reference.elgg.org/sessions_8php.html#a53c6256e03ff06499e017c37ffc7fd3b

By coincidence I've just uploaded a plugin you might be interested in: http://community.elgg.org/plugins/1640707/1.8.0/elgg-1819-news.

It's a "News" plugin - based on the Blog plugin - that only allows admins and group owners to post news / announcements (separate from blogs). You could still use the Blog plugin to allow normal members to make blog postings. Or you could take a look at the code of my plugin to see how the restriction to admin postings only is done. If you want to disallow group owners (who are no admins) to make postings you would need to make some additional modifications though.

As that isn't a function of the default topbar there won't be the required css for rendering a dropdown menu.  You'll have to provide your own.  Inspect the topbar to make sure your menu is being rendered, then add in the appropriate css to hide the menu until you're hovering on it.

This theme may be helpful for you 

http://community.elgg.org/plugins/1590632/1/simple-blue-white-theme-18x

this is a plugin that provides a dropdown menu from the topbar, you could adapt it.
http://community.elgg.org/plugins/1301890/0.2.2/add-new-items-dropdown-menu

elgg_register_plugin_hook_handler('entity:icon:url', 'user', 'my_plugin_avatar_url');

See the profile_override_avatar_url function in the core profile plugin for an example of how to use the hook

Thanks Matt. Based on your advise, I overrode icondirect.php and specified the path to my icons. However, I did not have to add "elgg_register_plugin_hook_handler('entity:icon:url', 'user', 'my_plugin_avatar_url')" to the start.php of my theme.

Hi. As per my earlier comment. The elgg site used the default images I overrode. When I replaced the default images, the site loaded the original images and ignored the ones I had in my theme. I had to do a full implementation as suggested by Matt. Now everything is working perfectly.