Christine on "Adding div with bg image to header.php"

If you're using a child theme, then you could insert an images folder in your child theme, but just to make sure, I would use the full url.

So use - background-image:url (http://justiceforchloe.com/wp-content/themes/colorway_child/images/fb_icon.png);

if you want the fb logo to appear to the right, you should use:

.fb-header {
height: 120px;
width: 156px;
background-image:url (http://justiceforchloe.com/wp-content/themes/colorway_child/images/fb_icon.png);
float:right;
}

Also I see that you've added padding-left. Just get rid of that. That's what's causing the box to be so big