In order to use fulltext search, you need to change the wp_posts table from InnoDB engine to MyIsam. But if you have less then 20 000 posts I would not recommend doing that, as you won't see any difference in search speed or results. Fulltext search is more for advanced developers, I hihgly recommend not changing anything in the databse unless you are experienced with MySQL.
You can read a quick guide about innodb to myIsam conversion here: https://rtcamp.com/tutorials/mysql/innodb-to-myisam/
But once again, unless you are experienced with mySQL, I don't recommend changin the engine.
As for the second isse, I will do a debugging soon to see why is that happening. The search might not work sometimes because of that.
Thank you for the detailed description and the proper login details, it makes my work a lot faster.Best,
If you like my products, don't forget to rate them on codecanyon :)