I would love to help, but custom coding is far beyond our support, I hope you understand that.
The issue seems to be this line:
'add_args' => array_map( 'urlencode', $query_args ),
I don’t know what that does, but maybe removing the urlencode will do the trick, I don’t know:
'add_args' => $query_args ,
You can probably even remove that line, apparently it’s happens with all search plugins too.