There was something similar to this today with the weatherman Steve Jarve. The rain and clouds were just glitched out, squarish blobs on the map and they were odd colors so you couldn't tell what you were looking at, and he's all 'you can see over here this and this is happening'. So whatever it is the weather people see, it's not what the audience is shown.
No, It is - They have monitors that show the air feed. It's a very easy thing to provide. Most will have at least 2 air moniters - one on the camera (Which uses the same monitor as the teleprompter), and one off to the left or right (whichever one they usualy face when they are waving their hands around at the map.)