You could easily modify the css/html/php to edit your header. For example, you could create a new <div> for a Logo in your header like this: the following code would go into your style.css (keep it in the #header for obvious reasons...
And then tie it into the existing class like this:
this goes in the header.php...
<div id="header-logo" class="container"><img src="http://your-image-goes-here.png"/><a href="http://androidfilesharing.com/"></a></div></a>
The above modification would give your primary menu at the top of the page, a header logo below the menu and then your content would follow below the logo. You could obviously modify this to your liking but I did this on my site http://androidfilesharing.com. And you don't have to worry about it maintaining responsiveness as the developer did a great job with that!
The possibilities are endless! The developer has provided a great foundation for which we can build upon. The sky is the limit!