Modifying PHP in child theme

I have set up a child theme for Refur and I am stuck on a few modifications.

1) the theme has a php for a page header image for sub pages. I want to try to replace this with a different pages header image for each page, but despite all my best efforts (including modifying the ‘custom-header.php’ file in the parent theme and adding a new file with the same name to the child theme), I cannot get this to work. Can you please let me know how to achieve this change? Which files to edit?

2) the featured image on the blog seems to be resized to 210*710px. Despite adding some CSS to the pages in questions I cannot seem to alter this image so that the featured image resizes to a more suitable ratio for the images (16×9)

The site I am working on is our new website here:

http://wordpress2015.wilddogworld.com/wordpress/

Thanks for any help.