Assumption: you are referring to resource identity.
1. We can guess what drives Facebook/google/tweet buttons from configuration of these buttons. Its safe to assume configuration that the identity input is the URL itself. I am sure they probably generate guid or some other id out of the URL (SHA/MD5 or any other scheme) which gets persisted in their system. For BC fb/g+/tweet buttons, dynamic URL is based on the postid which gets sent to fb/g+ etc.
2. Don't know. But URL by definition is guaranteed to be unique. It can always serve as the primary key to identify a resource.
3. As far as I know, resource identification is always done on unique URL.
4. As I said, URL can always serve identity of an html resource. But if you are referring to other form identities, e.g. user identity then there is nothing special other than session based cookies. As far as I know html5 doesn't add anything extra for session or data persistence. Facebook and google session cookies are visible to you from dev tools in ie or firefox.
My 2cents, not sure if was helpful