Notification that the admin is online

This should get you started. I’ve used a timeout of 5 minutes to allow for time sitting idle on the website. You could improve the accuracy with a script (if the current user is the admin) & pinging an AJAX request every few minutes to update the admin_last_seen timestamp.

/**
 * Check if the admin was last online at least 5 minutes ago.
 * 
 * @return bool
 */
function wpse_140253_is_admin_online() {
    if ( false === $last_seen = get_option( 'admin_last_seen' ) )
        update_option( 'admin_last_seen', $last_seen = 0 );
    elseif ( $last_seen )
        return $last_seen + 5 * MINUTE_IN_SECONDS > time();
    return false;
}

/**
 * Update "admin_last_seen" timestamp.
 * 
 * @link http://wordpress.stackexchange.com/q/140253/1685
 */
function wpse_140253_update_admin_online_status() {
    if ( current_user_can( 'manage_options' ) /* Might be better to check user ID if you have multiple admins */ ) {
        if ( ! $last_seen = get_option( 'admin_last_seen' ) )
            $last_seen = 0;

        // Only make a database update if last seen greater than timeout.
        if ( $last_seen + 5 * MINUTE_IN_SECONDS < time() )
            update_option( 'admin_last_seen', time() ); 
    }       
}

add_action( 'init', 'wpse_140253_update_admin_online_status' );

And in use:

<?php if ( wpse_140253_is_admin_online() ) : ?>
     <div class="message">Admin is online!</div>
<?php endif ?>