If I hire someone with a F1 or F2 visa to work as our nanny... what are the tax rules? Do I pay taxes on her? Does she pay taxes?

If you hire someone on a F-1 or F-2 visa to work, they are violating the provisions of their visa which prohibits them from working without authorization in a field NOT related to their field of study (for the F-1 visa holder).

That said, if you employed them anyway, they WOULD be liable for all of the taxes that a U.S. citizen would be liable for.