This page. provides some good tools for recording the screen (most of them with audio support as well) for Linux, Mac and Windows.
Picture in picture screen recording on Mac with Quicktime (PDF)
Video Overlay – Creating a Picture-in-Picture Effect (ActivePresenter On Windows) (PDF)
WebcamStudio For GNU/Linux: Screen recoding with PIP (picture in picture) on Linux
You can use webcam studio.
15 Best Linux Screen Recorder and How to Install those on Ubuntu —PDF
8 Best Screen Recorders for Windows 10 – Free & Paid (2019 rev.) — PDF

Mac – QuickTime Player can do a great job for screen recording with audio, check here (PDF).