I am a mechanical engineer and thus can't really help you with your second question but I have done several projects with sound and can help you with the first part of your question.
The tool you need is known as a spectrum analyzer, and is commonly used for measuring and testing waveforms of all types, including sound waves. What you would be looking for is what is known as the frequency response, or how different sound sources reproduce given waveforms. For example, some might emphasize higher tones, while others might emphasize bass (lower frequencies). The spectrum analyzer, which graphically displays the amplitude (quantity) of various frequencies, is coupled to a laboratory or instrumentation-quality microphone. This microphone is calibrated with a perfectly flat response (it receives all frequencies equally) to avoid contaminating the data with its own bias. To further remove outside influences, you'll need access to an anechoic chamber, which is a fancy name for a soundproof room with no echo. This will contain the microphone and the test sound source. Finally, you'll need some standard test tones or a frequency generator to generate the sound signals against which to test.
Your best source for this equipment and help with your project would be to find an audio engineer willing to help you. Many audio engineers work for recording studios, performance groups, and commercial sound and theater production companies. Music stores and audio equipment rental shops are also good sources. If someone who works there doesn't have the skills or equipment, chances are good they will know someone who does. An audio engineer will be familiar with what you are trying to accomplish, and have the equipment and skills to get good data. They do this all the time, for example, finding the particular audio characteristics of a speaker, microphone, or concert hall. An audio engineer is also likely to have a wide selection of headphones and other audio sources to test. Once you learn more about the process of testing audio equipment, you might try visiting an electronics flea market and finding some used equipment. Chances are that you will get better data with state of the art professional equipment, but sometimes its fun to do further explorations by yourself.
Let me know if you have further questions, and good luck with your project