I hope you are well today and thank you for your question.

Could you please share a screenshot of the screen where you have assigned the taxonomy to post or product?

Please make sure that you have configured the search form to search taxonomy as shown in the attached screenshot.

Are you using Default WordPress Search Engine or Inverted Index Search Engine?

Best regards,
Ivory Search Support

You can overwrite the plugin template file to make changes to it.

The below plugin template file displays AJAX search results and you can overwrite it in your child theme.

/add-search-to-menu/public/partials/is-ajax-results.php

Just copy the file and paste it into the root directory of your child theme.

I hope you are well today and thank you for your question.

Currently, the Ivory Search plugin does not provide this functionality but I will consider implementing it in the future version of the plugin.

Best regards,
Ivory Search Support

I hope you are well today and thank you for your question.

Are you using the same search form twice on the page?

Could you please share your site URL where it’s happening so I can troubleshoot it?

Best regards,
Ivory Search Support

I hope you are well today and thank you for your question.

You can add the search bar to the menu as described below.

Display Search Form In Menu

Best regards,
Ivory Search Support