The wrapping machines of Santa

Christmas is coming and Santa is working hard to wrap all the presents until the 24th of December.

He has six wrapping machines: A, B, C, D, E and F, that work $24/7$ all at the same time. But the harsh weather of the North Pole keeps breaking the machines. Each machine has a panel that indicates the state of one or two other machines. However, if that machine is broken itself, the displayed information on its panel may not be true. However, if a machine is working properly, its panel displays valid information.
The elves made a Main Control Panel so Santa can track all the six individual panels at once. On a certain day, Santa sees the this display on the Main Control:

PROBLEM 01:
Given this display, is there any way of having just one broken machine?

PROBLEM 02:
If Santa has two broken machines, which ones are they?

This is an old puzzle from a book I had when I was a kid.