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

You can configure the search form to achieve it as described in the below page.

Search Media Files Or Attachments

Best regards,
Ivory Search Support

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

The search form and its text field are displayed by the theme that you are using on your site so you can change it by editing theme searchform.php file in the child theme as described in the following page.

How to create a custom search form in WordPress

Best regards,
Ivory Search Support

I could confirm the issue on your shared site.

Please try resetting the search form on your site on clicking on the Reset button of search form.

This can be due to plugin conflict on your site so please try temporary deactivating all plugins except Ivory Search plugin and see whether everything works fine and then enable the plugins one by one to see which plugin is conflicting if any.

Would you mind if I log in to your site and do some troubleshooting? If this is ok then could you please share me your site log in details privately by checking the option “Set as private reply” when replying to this topic?

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

It depends on how you have configured the search form settings so please make sure you have configured it correctly referring the information provided in the below page.

Documentation

Also, please try resetting the search form by clicking on the Reset button and then configure the search form.

If it still doesn’t work then could you please share me the screenshots of the search form settings that you have configured?

Would you mind if I log in to your site and do some troubleshooting? If this is ok then could you please share me your site log in details privately by checking the option “Set as private reply” when replying to this topic?

Best regards,
Ivory Search Support

You can achieve this by removing the above shared CSS code and using below CSS code.

#mega-menu-wrap-main-nav .is-menu input.search-field {
    float: left;
    margin: 0;
}

#mega-menu-wrap-main-nav .is-menu .search-submit {
    padding: 11px 10px;
    min-width: 0;
    font-size: 14px;
    float: left;
    height: auto;
    line-height: 14px;
    margin: 0;
}

#mega-menu-wrap-main-nav .is-menu  .search-close {
    top: 38px;
    right: 8px;
}