Download OBS: https://obsproject.com/
OBS VirtualCam (for use with Zoom): https://obsproject.com/forum/resources/obs-virtualcam.539/
Using OBS, we can do lectures live on Zoom with a face + document cam, as well as record the lectures without recording the entire Zoom meeting and everyone in it.
Download and install OBS. After launching it, run the auto-configuration wizard (which should pop right up). Select Optimize for Recording, default Video Settings, and click OK through the rest of the installation. Close OBS, then download and install the VirtualCam plugin. If it says that the obs-studio folder already exists, override it and allow it to install to that folder. When prompted, select the option to only register 1 virtual camera, and click through the rest of the install.
Open OBS, and add sources in the bottom right. Video Capture Devices are cameras, so that will be the correct format for document and face cameras, but there are a ton of other options, such as showing a browser window, static image, or video. Once you have the sources you want, you can move them around, resize them, and reorder them in the canvas in the middle of the screen. If necessary you can also "crop" videos by holding the Alt key when resizing.
Make sure that the Audio Mixer is only using the microphone you want to use. By default it will use your system audio and a default mic. You can mute system audio in the mixer and add microphones in the Sources tab from Audio Input Capture. Ensure that only the mic you want to use is unmuted.
Open the Tools tab on the top and click on VirtualCam. Select Horizontal Flip (since Zoom will automatically flip your video, you will need to undo their flip) and based on preference you can select AutoStart as well.
Open up OBS, format your lecture, and start VirtualCam from the Tools menu if it hasn't already been autostarted. Click "Start Recording" in the bottom right of OBS to begin recording the lecture to your hard drive, then open up Zoom (or whatever service you use). Select OBS-Camera from the camera options and you should be good to go!