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One of my favorite “decision helpers” in design is the Principle of Least Surprise: try to avoid system behavior that your users don’t expect. (Yes, sometimes this is pretty straight-forward, and at other times it’ll take lots of usability testing to find out what, exactly, users expect. 😉 )
You already noted that options 2 and 3 violate that principle.
In contrast, option 1 is very common pattern that can be generalized like so: allow users to navigate to an empty container (a folder, a page, a tab view, etc.), but clearly indicate that it is empty.
To help them decide whether a container is worth opening, you can display the number of contained items in the context of the navigation control that takes users to that container.
Here’s a simple example from Apple Mail: The selected Inbox folder is empty, and the main content area displays an explicit notice. Other folders display the number of unread messages they contain.
Applied to your design problem, you could implement option 1 and add the number of available analytics graphs to the sub-navigation tab labels. Something like this:
Mike M’s approach is another good option, but I just find it that little bit more restrictive.