Homepage Header Image Settings

This is actually a theme question – you’ll need to modify the theme to put an image in the header as you are describing. It’s possible to code it so it only appears on one page. Also, you should not modify theme files in a default theme – as the changes will be lost when WP is updated – so you’ll need to start by creating a child theme – https://codex.www.ads-software.com/Child_Themes

Once you have the child theme set up (or if you need help with it), post on the twentytwelve theme forum and someone can help you with the specifics.