Eyria

Credits for the great header pic: Pixabay, user Salao228, Meer, Sonnenuntergang.
Eyria gives you the possibility to choose between a big header with fixed height or a full-height frontpage header. It is a free skin for Dynamik Website Builder, a childtheme of Genesis, which means you have to own and install both of them to use it. Genesis is a Wordpress framework.
The carousel you see in use here is the free Responsive Posts Carousel). It lets you to display Posts, WooCommerce Products or any other Custom Post Type as Carousel. You can use from a bunch of pre made styles for post thumbnails and featured images. You can also create carousel for just post titles without having thumbnails. I´m using the Feature Top area to display it on this page. You will find some more infos about Eyria on the Documentation and About pages.