Different Headers on the page

Hi, can you help?

I am after a full width header image on the homepage, and then different header images on other pages but at the moment I can only create headers with the widged, if I have the search bar activated (which is ok)

but only if I also place an image in the header (top right of the home page).

Then the same image is palced throughout.

I want to replicate the demo home page,(with out the black box),
https://demo.ilovewp.com/?theme=faith

And tis page for the rest of my other pages
https://demo.ilovewp.com/faith/page-templates/reversed-sidebar/

I can’t seem to find much in the documentation. Hope you can help!

The page I need help with: [log in to see the link]