Display information from Arduino Serial Monitor

From what I understand, you can’t have processing functioning at 100% while the Arduino serial monitor is open. The Arduino serial monitor has some information that I need to be able to see written to it, is there a way to have the processing app read/duplicate and display whatever is in being written to the serial monitor so I can check it if I need to?

the serial port can only be used by one app,
so you close the arduino IDE serial monitor
open the processing and run the example from serial library like
so all the arduino sends will be printed to canvas.
that was the easy part, if you want use keypressed and send to arduino some Strings
it is a little bit longer way.

The Arduino serial monitor does not affect the performance of Processing.

I have an Arduino Mega 2560 R3 which has multiple serial ports.
If your flavor of Arduino does not have additional serial ports you can use:

You will need something like this to use this additional serial port:

I have also used an Arduino Uno as a serial adaptor:

And voila!
You can now display data on your Arduino serial monitor and also send the same data to an additional COM port that can be Processing in this case.
You will have to modify your code to use two serial ports on the Arduino side.
I do this often as a demo.

If you write code correctly on the Processing side you are making your own serial monitor with Processing; you can only connect the Arduino serial output to one or the other and not both at the same time.
Processing has this example which can be simplified (remove the fonts) to do be a serial monitor using println() to console: