The Header image should also hyperlink to the home page.
Header images do not link to the blog URL.
No and no: header images don't have to link to the blog URL (when the blog title does, or when there's a Home item in the top menu), but on many themes they do.
Since you have the Custom Design upgrade, what you're looking for is possible, only you need to ask about it in the CSS forum, not the Themes forum.
(You'll also need to correct the positioning of the header image. On Expound it's designed to display its middle part on lower resolution screens and narrow devices: drag the browser window to make it narrower and see what happens.)