@mmglisci: Looks like you are totally confused with the WordPress system. In WordPress we have two option for Homepage(Front page displays) that you can set from “Settings => Readings”
1. Your latest posts, where all your post will be displayed as blog.
2. A Static “Front page”, where you can set static page in homepage.
So, when I check in your site today I see that you have latest posts mode. So, there is no home page and there is not way to edit that page and it will not be in your page list.
Also when you build custom menu, you can add and remove the menu item you like. See this article http://catchthemes.com/blog/custom-menus-wordpress-themes/
I am not sure what are you talking about the image below the menu. Do you mean the Featured Post Slider. Then for that also you need to create post and add featured image in that post. Then you need to ID of that post in “Appearance => Theme Options => Featured Post Slider”. See the theme instruction page http://catchthemes.com/theme-instructions/simple-catch/ for more details