Can I simultaneously record video from a MacBook webcam and the iPhone screen? So I know I can use QuickTime to record a movie from my Mac's webcam.

And I know I can use QuickTime to record a movie from the screen of my iPhone, connected via a USB cable.

But my question is: can I use QuickTime, or some other application, to record both videos simultaneously?

And can I use QuickTime, or some other application, to combine the videos, so that the video of the iPhone screen is shrunk down into the bottom right corner of the video from the webcam?
You can open a second instance of QuickTime using
$ open -n -a QuickTime\ Player
#       │  └ Specifies the argument is an application to open rather than file.
#       └ Open a new instance of the application even if one is already running.

Each instance can start a New Movie Recording with different inputs.
You can then use iMovie to combine the two videos, using Picture in Picture:
Create a picture-in-picture effect in iMovie on Mac