Yep, it can be 'hidden' with the menu bar. They specifically mentioned and showed it in the keynote.

Probably - some of the marketing shots they showed in the event showed it being hidden with a black bar, but I couldn't find any that showed the toolbar itself being below the notch. At any rate, if it doesn't exist at launch, someone will make an app for it.

And if Apple doesn't provide that app, it will break after every update.

Also: Can the mouse pointer be "hidden" (moved) under the notch?

Yes. Tim said the notch looks great in dark mode.