1. Complex search
From what I can understand you want to integrate the plugin somehow with the existing layout and functionality.
You can simply just replace the search there with the plugin shortcode, and enable redirection to redirect the user when clicking the search button or hitting the return key. It will then open the same page, passing the search phrase as the normal search would.
At the same time you can keep the ajax functionality when the user types into the search bar.
Deeper integration – like integrating the ajax results into the tabs separately, are only possible by customizing the plugin, probably a good amount of work.
2. Live site issue
This is simply a missing file problem as the error indicates. Try checking the permissions as well on that file. Wrong permissions might lead to this error message. It is also possible that the copy was not complete (FTP is very unreliable) so deleting and re-copying the file should solve the problem.
If that does not help, re-installing the plugin is the safest option, and it always helps.
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