Yes. This has happened to me. Apple sends your submission through a light testing regime by a human. If they pick up an egregious bug or substantially incomplete feature, they may reject your submission.

You could change the verbiage on the button to make it clear the feature is not yet implemented, which would probably pass.

One suggestion is to have a live blog and link to discussions, using a redirect from your web server to track which button was pressed in the app. This way, reviewers arrive at a logical page while you could track which version of the app was used. Why risk rejection for submitting something with an incomplete feature when you can have a simple "coming soon" link before you submit your app for review?

Only if there are already tons of apps that will let you navigate, say, The Smithsonian Museum of Natural History." Then that one app for the smithsonian MAY be rejected.

But, I suspect there are not, so you should be fine.

Similarly, since you'll presumably be adding additional apps with different functionality, say the next one is for the Guggenheim, you should be fine. The 2 apps couldn't possibly be used as a replacement for each other.

Apple's concern here is keeping out over-served functionality. There are so many "fart" apps that yet-another-one can't possibly help any user anywhere beyond what's already available. Museum apps are well outside of that scope, assuming you create a quality app with a great UI for museums that don't already have several hundred apps.