Extremely low output from amplifier
That circuit helps a lot.   So a few things.  I'd move R4 (10k ohm power supply splitter) down so that it didn't block the 9V from the 3.3k mic bias resistor. 

Second I don't think the 100nF coupling cap is big enough.  You're loosing signal through the 3.3k bais resistor and then through the 4.7uF cap on the non-inverting input. (or on 9V rail once R4 is moved.)  Calculate the corner frequency of 3.3k and 100nF.  There's a similar voltage divider on the output, with a 10k resistor.  

Oops!  Well I don't know the LM386 either!  One thing I will observe looking at the LM386 spec sheet.  All the amp circuits show 10 ohm in series with 0.05uF on the output.  I couldn't find a reason for this in the rather thin section on "Application Hints".  But you might try adding it.