Hello kreeper124,
Yes, you can record the screen with the PC sound, your voice from the microphone, and your face from the webcam at the same time in different files for each.
Please refer to the following links below and try the functions with the free version.
1. Enable the "Save webcam video as separate file (.mp4) option.
https://www.bandicam.com/how-to/webcam-overlay/
2. See "How to record computer and microphone sound separately" and enable the "Save audio tracks while recording (.wav)" option.
https://www.bandicam.com/support/tips/two-sound-mixing/
Thank you.