Is the sound at the Metropolitan Opera house in NYC amplified OR are
the divas really able to project unaided?

Most of the divas sing unaided.  Back in the era when the Met was
denying that anyone used mikes, there were a few famous incidents
where a certain black soprano was caught with her microphone turned on
backstage and her comments coming through the sound system.  The Met
hemmed and hawed for a while and then said that there was a "sound
redistribution" system used only to sweeten the dead spots in the
hall.

Of course nobody believed them.  Mostly because no one but the one
soprano was ever caught using a mike.