we tested your plugin with our SearchEverything plugin and noticed that our plugin doesn't return any search results for FAQ entries.
We figured out that this this happens because your plugin doesn't explicitly allow searching. To allow/enable it all you have to do is to add
exclude_from_search=>false to arguments you pass to the
register_post_type() function - file classes/class-faq.php (args, line 33)
If you need more details, I'll gladly help.