I need to totally customise WooCommerce checkout page. I can do a lot of things with Woocommerce programatically but this one is not an easy task since I need to divide these fields just like on the picture below.
Website is on this link: https://2houragency.com/. I can see that they have hidden some default Woocommerce HTML elements and created their own, but I am not sure how to do it by myself. And Wocommerce is not that easy to customise for this kind of pages.
Get into the templating documentation of WooCommerce here. You'll probably want to use one of these template files to re-order/structure the checkout template.
You can find even more information in the Code Refference.