That you can achieve by configuring the search form as shown in the attached screenshot.

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

#site-navigation {
    width: 100%;
}
.main-navigation li.is-menu {
    float: right;
}

The search results page is displayed by the search.php file of the theme that you are using on your site so the plugin doesn’t control how the products will be displayed on the search results page but your site theme controls it.

You can change this developing custom code in the search.php file of your child theme 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/

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

Do you mean on the search results page or in the AJAX search results?

Best regards,
Ivory Search Support

I have already done the test with twenty twenty one and indeed it works well, there must indeed be a problem with my personalized theme, I cannot share the link of my site because I work in localhost, but I can share screenshots of my code.

If it is your theme issue then please contact the theme support to resolve it.

I’m a junior web developer and I wanted to take care of page redirection myself, so what do you mean by custom code? What code and where?

The custom code means you have to develop code yourself to achieve this. There is no already developed code or solution for it.