Could you please share the page URL from your site where it is happening so I can troubleshoot it?

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

You can deselect media in the search form Post Types section as shown in the attached screenshot.

Best regards,
Ivory Search Support

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

Could you please try using Full-Width menu search option as shown in the attached screenshot?

Best regards,
Ivory Search Support

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

You can achieve this by adding the below CSS code in the Custom CSS option of Ivory Search plugin settings on the path Admin Area -> Ivory Search -> Settings -> Settings

div.is-ajax-search-details, 
div.is-ajax-search-result {
    padding: 2px;
}

Best regards,
Ivory Search Support

To modify the width and height, You have to develop custom CSS code and add it in the Custom CSS option of Ivory Search plugin settings on the path Admin Area -> Ivory Search -> Settings -> Settings

I can help you to develop CSS code if the search bar on your website is accessible to me.