I think you are referring to the border that’s there in between title and image. To remove that please add following CSS under X > Theme Options > CSS:
Last thing regarding the Icon 3 and the side bar on the homepage:
When I try to edit the homepage in Cornerstone, the only thing that shows up is the content in the side bar (managed by widgets), but not the main body of the home page.
Is there a way to edit this page with Cornerstone?
Pages that are created outside the Cornerstone are not editable in Cornerstone and vice versa. I checked your homepage and it’s not built with Cornerstone so you cannot edit it in Cornerstone. You can re-create a page from scratch in Cornerstone if you’d like to switch the editor.