Certain header elements not served over https

I’m not sure about the first one, the profile, but the rel="alternate"s and the rel="shortlink" provide different formats for different readers, like XML and RSS feeds. These should be generated by your site URL. In your dashboard, go to Settings > General, and make sure you’re using https:// instead of http:// in the URL. You may then need to clear your site cache to see the change.