BuddyPress.org

Just to clarify – you should not be moving any themes from the BuddyPress directory. From WordPress 2.9 onwards the themes will be automatically detected in the BuddyPress plugin folder. You can simply create a new child theme in wp-content/themes and it will automatically know that the parent is in the BuddyPress plugin folder.

Mike: Not sure why you want to remove the custom header functions? They simply provide a UI to uploading a custom header image in Appearance > Custom Header.