This is going to require theme edits and/or a custom theme. I would be happy to build this for you for free if you’ll host the site with me. You can contact me at [email protected]
You cannot create a sticky header without doing theme edits. Depending on whether you are doing a CSS or jquery approach you will either need to edit the stylesheet, header.php, or possibly both files.
In the Appearance -> Menus section you’ll need to create your links using the “custom links” box. (www.example.com#section) The only real page in your menu should be “Home”.
You can distribute the section tags through the code editor within the WYSIWIG editor. So long as you wrap each section in a div you could even apply custom backgrounds to each section while still retaining the ability to edit the content in the WP page editor.
