I can be taught! But in the mean time...

[k7elp60]

Here's a new list:

2. It needs to fit in a tiny tiny place.

Drew

You might tell us the physical dimensons to the tiny tiny place.
A pair of A76 batteries would be approximately 1/2" in diameter and about 1/2" tall. It is possible to solder all the components together without a circuit board.

 

[audioguru]

The mic and its amplifier will be powered all the time draining the tiny battery unless you add additional circuits to pulse them on and off.

With a current of only 190uA the voltage of an A76 cell drops quicky to only 1.4V. Very few opamps work from a supply of only 2.8V.