"Recent Posts" and "Recent Comments" showing up in header??

Does that theme come with a section in the dashboard named, “Custom CSS”, “Custom Styles” or “Jetpack”, or are you using a Child Theme?

In Jetpack’s Custom CSS section of the dashboard, enter this;

#sidebar-header {
 display: none;
}

Whoopsies, we can amend that.
Instead of that code I recommended, try this;

.widget_recent_entries,
.widget_recent_comments {
 display: none;
}

Okay, how about this instead;

header #archives-2,
header #categories-2,
header #meta-2 {
 display: none;
}

I’m getting confused here, I swear the page keeps changing its structure after I recommend CSS.

1 second

Edit: How about this CSS instead;

#sidebar-header aside {
 display: none;
}

#sidebar-header aside:first-child {
 display: block;
}

There’s so much white space in the header because of these two divs;

<div id="sidebar-header" class="widget-area" role="complementary">

(screenshot http://snag.gy/Ltni2.jpg )

and

<div id="site-title">

(screenshot http://snag.gy/BFP7z.jpg )

You can explore this too using a browser developer tool like the one built-in to Chrome.

Reduce the width on your #sidebar-header element;
E.g use this

#sidebar-header {
 width: auto;
}

And Thanks for contributing to the WordPress.org community! Really, this thread will help a lot of people with the same issue.