Make sure you have allowed camera access in your browser. Check if another program (Zoom, Skype) is using the camera.
This depends on the lighting and the quality of your camera. Add light in front of you and wipe the lens.
It’s more convenient than a mirror if you don’t have one nearby. And unlike the phone’s camera, the image is mirrored (flipped) as you are used to seeing.
No, the microphone is not used and is not recorded. Only the image.