Problem at audio output pin with electret microphone
You can't reach your stated goals the way you are trying to go.


You appear to have the "envelope" output connected to the Arduino, but say you want the wave rather than the envelope.  Connect the "audio" output to the Arduino.
Sampling with the Arduino the way you are, you will never get anything that looks like digitized audio out of the comport.  You can get (maybe) 300 samples per second the way you have that written.  That allows a total audio bandwidth of less than 150Hz.  That is around the highest tones of a subwoofer.  Not much speech to be had there.




If you connect the "audio" output to your analog input on the Arduino, then it should show values around 500 when it is quiet.  The detector board has the audio "floating" on 2.5VDC, which is half of the Arduino input range - half of 1024 is 512.

You picture actually shows no connection between the detector and the analog in on the Arduino.

You can solder the wires to the detector.  That would work better than "poke 'em through and pray."



You've updated your question.

Capturing and then transmitting all in one block is better.

It still won't get you very far.  

The Arduino has 2 kilobytes of RAM.  So, after less than one fourth of a second, the RAM is full.  Transmitting that block of data over the serial port will take while, and you can't sample and transmit data at the same time if you want to sample as fast as possible.