Yes, no sound is recorded. Access to the user's mic isn't possible without a permission. If there are sections of the website or paper that seem to imply that, let me know and we'll clarify.
It does, and also as someone who has never heard of AudioContext before, I can't fathom why it would be necessary for a web application to generate an audio data stream that isn't output to speakers _AND_ _THEN_ analyze the result.
What is the typical use case for AudioContext?
The capabilities of AudioContext used in audio fingerprinting seem like they're beyond what is really necessary?
AudioContext is actually pretty cool. As far as I know, only Firefox supports it at the moment. But it allows you to work with audio streams in raw byteform, which means you can do advanced audio processing in client side javascript.