How to analyze reverb in existing sound recording? I'm wondering if there is a technique by which to analyze an existing sound recording and extract some details of the reverb and echo that are present (either due to natural environment, or added during production). 

Are there software packages or libraries that implement that sort of analysis? (Is there even a chance of recovering the audio minus the reverb?)
You may be able to reverse engineer the reverb if you have a segment of relatively clean reverb 'tail'. This will allow you to play around and get some metrics such as decay time and frequency response.

Convolution reverb works by recording an impulse response in a particular location/machine after a burst of noise. This is then convolved with the input signal to apply the reverb.