It's purely software. An update with audio routing will be out likely this week (it's in testing, and you can already get it if you compile stuff yourself).
My understanding is that the microphone (& speakers?) isn't wired directly to the modem, but needs the CPU to replay the audio to the modem so that the modem (aka, baseband) doesn't have access to the microphone audio except when it actually needs it. So, I would think that the headphone mic wouldn't work either.
This is good for privacy, but can this way of not wiring the microphone directly would also be helpful to do recordings and to send/receive faxes, or does that not work?
Normal phones can record phone calls, right? I assume that this wouldn't make anything possible that isn't already possible. But, again, I really don't know what I'm talking about here, this is just my understanding from what I've read.
Before I bought a Xiaomi it was impossible to record any call (Samsung, HTC) and it seems it was by design. The only way was installing an app that somehow routed the recording through their servers (no, thanks) otherwise you could only record outgoing (or was it incoming?) sound.
Usually phones have their modems tightly integrated within SoCs, so audio is both directly connected to the modem and accessible to the CPU.
My understanding is that, in general, it's not possible to send a fax via cell phone audio because the digital compression applied does not pass enough information to sustain a fax modem connection. It may be possible with a higher-bandwidth thing like voice-over-LTE, though? (of course I'd love to be wrong and learn that this is easy :-)
CSD data calls are perfectly possible in GSM - your carrier can disallow them though. However, you usually feed and receive data to/from the modem in a different way than via its audio interface ;) Other than that, you're right. It's possible to come up with a way to pass data through GSM codec, but it definitely won't be a regular FAX connection then.