Ok for the regulator, that should work just fine.
Regarding the place to insert the Teensy, here are my thoughts: If you have an AGC then before the volume control as you mentioned should be just fine.
But if you don't, you may have significant variations in signal levels. If placed after the volume control at least you apply some level control manually. Just a thought.
Also I would not worry about impedance matching until you test it. Just make sure it is AC coupled through capacitors.
For the serial part: in the Nano the USB chip's serial lines are connected via 1K Ohm resistors to the D0 and D1 lines. So you can hook up a TTL serial line there but you have to be mindful of the pull-up effect of the USB chip.
You can hook up the Teensy's RX and TX lines directly to the TX (D1) and RX (D0) lines (respectively) of the Nano since the Teensy 3.2 is 5v tolerant on its digital pins (which are shared with serial 1, 2 and 3). You may have to insert a 3.3V to 5V level converter for the Teensy's TX to the Nano's RX as the level may be on the low side of the specs for the Nano, but most of the time it just works. If you have an oscilloscope it is easy to see what the levels are when sending serial data.
But, keep in mind that as long as the Teensy is connected to the D0/D1 Nano lines it will prevent communicating to the Nano via the USB port (like for programming). Best would be a switch to disconnect at least the TX line from the Teensy or better both TX and RX just to make sure, although just powering down the Teensy may also do the trick (hoping all lines go to high impedance then).
So I would start simple and add extra hardware if you run into issues.
I like the idea of using the Teensy for microphone compression. Please share your results when you get it working.
All the best,