How do I fix the missing top 1/2 inch of the content box?
The body class in the custom-media.css is defining margin-top: 90px for the fixed header, you will need to increase this to match the size of your header. 

You may need to include media queries to account for reactive menu changes.

It probably works when you are logged in because either the admin toolbar is modifying the margin or there is a rule specifically for being logged in that assumes the toolbar but you don't have it enabled.