Hey Jules, when you modified the CSS did you do it in a child theme, through a CSS plugin or directly in the WordPress Style.css file?
Also, have you made any modifications to your function.js file?
I took a look at your site and you have over 20 CSS files loading on your front page with 41 invalid CSS declarations, some of your plugins look a little suspicious, and your function.js file is missing about 7 lines of code at the bottom and showing one error.
The menu scrolling on the page and the search toggle are a products of the function.js and CSS. So there are a few possibilities. Any information you can provide on how you did your modification and what plugins you’re using would be helpful.