Static Front Page

When we first set up the Sydney theme, we were somehow able to do it without having a menu on the home page. Now, after the latest WP update, the theme has somehow reverted back to the original theme header photo and has added the primary menu to the homepage - which we only wanted to show on the inner pages.

How do we get the menu off the homepage and make the theme keep the images we use for the header even when there are WP updates?

The site is at