Hello,

1. You need to disable the Header clone https://xtemos.com/docs/woodmart/header-builder/global-header-settings/ and make the necessary rows sticky https://xtemos.com/docs/woodmart/header-builder/header-rows-columns-configuration/

2. Please add this code to the Theme Settings > Custom CSS > Desktop:

body .whb-column .woodmart-search-form input[type=text] {
    min-width: 200px;
	max-width:200px;
}
body .whb-column .woodmart-search-form {
max-width:252px;
}

Best Regards