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

Where do you want to display it exactly?

I visited your site and displays in the header for me as shown in the attached screenshot.

If you want to display it at the end of the menu then please display it in the menu and I will help you to reposition it.

Best regards,
Ivory Search Support

You can achieve this developing custom code in by contacting the theme author or consider hiring a developer to develop it for you. You can hire a developer from any freelance site or WordPress agency.

You can also consider hiring us to develop it for you using the form https://ivorysearch.com/custom-work/

You are most welcome, I’m glad I was able to help you with this matter. There is no obligation but by your kind words I wonder if I could trouble you to leave a review based on this experience here:

https://wordpress.org/support/plugin/add-search-to-menu/reviews/?filter=5

I’d really appreciate that. 🙂

And if I can be of any further assistance please don’t hesitate to ask.

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

when we search by author name, then in which posts content this author’s name is used, these posts showing in the top of the result and searched author posts is shown after that.

Yes, this is expected results as these both are different functionalities and work independently.

When you configure the plugin to order search results by author then it doesn’t consider the searched author posts.

Best regards,
Ivory Search Support

1) If I add the code you provided above to Custom CSS to add the “x” to close the nav menu Ivory Search box, once I start typing in the search bar, it superimposes over my theme’s “x” instead of overwriting it, as seen in the attached screenshot.

Then please try changing the above shared CSS code as following.

#masterhead .is-menu .search-close {
    right: 8px;
    top: 8px;
}

2) If I don’t use the code, my theme’s “x” shows up but doesn’t work to close the search bar. However, it does work to close the search bar in my sidebar widget.

I am not sure about the theme “x” so please contact the theme support to get more information about it.

3) In Ivory Search Settings/ Menu Search, if I disable the Display search form close icon, it doesn’t save and always reverts back to that option being toggled, whether or not I have the custom CSS code you provided added.

I have tested it on my test site and it’s working fine for me using the latest version of Ivory Search plugin.

Could you please try using a different browser?

4) With the sidebar widget, even if I remove the title “Ivory Search,” it still shows up.

I could confirm this issue which will be resolved in the next version of the plugin.

In the meantime, Do you want to hide the title on your site?

If yes then could you please share the page URL from your site where it is displaying so that I can help you to remove it?

I have a question: is there a way to give more weight to pages first and then posts in the search results? Is this a pro version setting or is it not available at all?

Yes, that option is available in the premium version of the plugin as shown in the attached screenshot.