I know how to create a backend page through the UI (../Sitefinity/Administration/BackendPages/Pages). Is there a way to add one through the project in VS so that I can create a custom MVC Admin Page with control over the controller and styled similar to the rest of the backend?
I would like to add a new section at the top in the backend similar to Dashboard, Pages, Content, Design or Administration which links to one custom MVC page.
Found a good solution to this in combination with Veselin's answer above. Once a page is created through the Sitefinity backend at ../Sitefinity/Administration/BackendPages/Pages you can add custom MVC widgets. In order to restrict widgets to only appear for the admin pages you can register them to the section 'Dashboard' that is only available for backend pages:
[ControllerToolboxItem(Name = "CustomAdminWidget", Title = "Custom Admin Widget", SectionName = "Dashboard", CssClass = "sfMvcIcn")]