One other thing to do is instead of hooking the 386 output to the arduino analog pin, hook it up to a small speaker and listen to the sound. When you are comfortable that the microphone amplifier section is working correctly then would be a good time to begin testing it with the arduino.
When dealing with electronic circuits it is better to work with small isolated parts independently and get them working properly. It is even important to do this with circuits you have built and tested before also because it is easy to diagnose problems in small well defined pieces.
Leave the testing of the whole designs to the very end of the process--you'll have enough problems with the butterfly effect on whole circuits with known working subcircuits.
On the Analog circuits and baud rates. The type of analog to digital converter used in the arduino does not perform an instaneous conversion--it uses a type od iteration to perform the conversion. This is why the conversions take up some period (up to ~250uS). When the conversion is complete you just read a register that contains a value between 0 and 1023. No serial communication is nescessary.