On CRT screens yes, but backlight in LCD screens is LED/fluorescent driven by much higher frequencies. Though some LCD screens still flicker, but it is visible only on special patterns: http://www.lagom.nl/lcd-test/inversion.php
Not necessary much higher. I've measured screen flickering in Lenovo T500 (probably one of the oldest laptops with LED backlight) with small solar cell and oscilloscope and it's 220Hz, with lowest brightness setting only 100Hz (although this brighness level is not too useful):
http://commonemitter.blogspot.com/2017/06/lenovo-t500-measur...
Screen refresh rate (rate that each image is replaced) is a lot different to the frequency of the PWM applied to the backlight. If the backlight were pulsing at 60Hz people would be _very_ upset.
Screen backlights aren't turned on and off at 60 Hz.
The screens have separate backlight which is done with other technologies and if with leds, definitely with higher frequencies than 60 Hz.