Can you clarify what you did to fix the header. as it looks like you have some bad CSS…
That said to make it work, you need to add a z-index to the header container. You can do that by adding the CSS rule below to the theme Global Custom CSS rule box
#header {z-index:3000;}
That said you should add a background color to the menu or when the content passes behind it becomes unreadable.
On a side note:
You have an empty info bar that should be hidden properly using the theme Option to hide the Info bar (MENU SECTION)
You also have an empty title and tagline. Ideally you want them to have content for them for the search engines, and you can hide them using the hide area option in the theme option for title and tagline.