I'm not able to provide temporary admin or FTP. Will you be able to provide some instructions for me to debug?
I've already deactivated all plugin, changed the theme to twentyfifteen but search is still not working. It does show “No Results” and if I enable redirecting to a result page, results are shown. But no result is show if I want it to return the result via AJAX. I've also turned an the compatibility functions as mentioned by you.
I'm searching a custom post type created by my theme. I've attached my theme files below. Thanks.