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.

Sorry to hear about the problem you are having.

I have tested it on my test site and it’s working fine for me using the latest version of the plugin and PHP 8.1.10

Please try deleting the plugin and reinstalling it.

Also, clear any cache if you are using any on your website,

Best Regards,
Ivory Search

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

You can achieve this by developing a custom code.

If you are not a developer, you can consider hiring a developer to develop it. You can hire a developer from any freelance site or WordPress agency.

You can also consider me developing it for you using the form https://ivorysearch.com/custom-work/

Best regards,
Ivory Search Support

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

It seems you have already optimized the search.

Are you having a huge product list?

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

Best regards,
Ivory Search Support

I visited your shared website and saw that your theme is hiding the mobile search icon.

You can display it 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

.is-menu svg.search-icon {
    display: block !important;
}