[A Squared]

No, it isn't right like that. The switch should not have any effect at all on how the outlet tests. The fact that the tester shows a fault on the outlet when the switch is closed indicates that something is connected incorrectly

Ditto the light coming on when the hair dryer is turned on. That should not happen.

If you switch the switch on and off with nothing plugged into the outlet, does the light turn on and off?

When the light came on when you ran the hair dryer, was the switch on or off?