Hello,
01. Try to use the Theme’s Layout Builder you can create Custom Layouts for WooCommerce pages like Shop, Category, Single Product page, Cart, and Checkouts. You can use the product categories widget in the layout and make it look like it.
Further, you can read more about the Layout Builder here: https://xtemos.com/docs-topic/woodmart-woocommerce-layout-builder/
02. You can use the Mailchimp widget in the Footer by editing the Footer HTML block.
https://ibb.co/5nFt2GS
03. You need to edit the footer html block with the page builder and change the icon size.
04. You are using the custom header on your site, Woodmart theme provides the option to create different headers for different pages.
https://xtemos.com/docs-topic/how-to-set-different-header-for-specific-page/
You can check the custom header for a shop page and add the menu items.
https://xtemos.com/docs-topic/options-for-pages/
Best Regards