To make the whole header image clickable to something else than the home page, use the header “Image HTML replacement” box with HTML like below
<a href="http://LinkURL"><img src="ImageUrl" /></a>
To add a button over the header image, you could use the Header HTML Area with the same HTML as above, then set its BG color to transparent, and CSS like below in the BG CSS+ box
{position:absolute;bottom:30px;right:10%;max-width:100px;}
Use either top or bottom and right or left for the position with pixel or % values. Make sure to test the responsiveness by changing the browser size to get the behavior you need.