Electronic – Debouncing this Rotary Encoder Switch

It depends on what the default state of the switch is. A capacitor will only charge when you give it a positive voltage. Usually, in an embedded environment, we use a pull-up to give a pin a default high state, and link the switch to ground. Adding a capacitor won't help here, because it won't "store" the ground state.

However, you can also use a pull-down. This would mean the pin is by default low. Making it high by pressing the switch, will charge the capacitor. After releasing, the capacitor will keep the pin high for a little while, so yes, this would work. I'm not sure if 1uF is enough, too little or too much, I'd recommend you to look with a scope and try it out a bit.

You need to transition on the screen going white within 0.5ms, transition on the screen going black within 10ms, but ignore periods of black lasting less than 4ms. This is more constraining than simple R/C circuits can provide: you need a timer.

The venerable 555 timer will do what you need. Set it up in monostable mode, with a duration of 6ms (make it adjustable), and drive the reset line from the output of your OPA141. Then, any glow from the screen will reset the timer, but if there's no light for 6ms then the output will go active. (You may have to play with the various polarities.)

An alternative would be using one of the simplest microcontrollers (e.g. an 8-pin PIC12) with an analog input. Less than $2, but incredibly versatile.