Correction! You are wrong. The more and more air you take out, the fainter, and fainter and fainter the sound will become. But the speed at which it propagates will remain the same. This is assuming that you would be able to heat the remaining air as you removed air, thus keeping the temperature constant with respect to the dropping pressure.

As far as the sos in a solid, verses a liquid:
Those are different substances. The sos is different in different substances. In steel, the molecules are arranged in actual crystal lattices. These lattices are tugged on by sound waves and sound waves will propagate much more directly because the molecules in the steel are physically coupled to one another. In a gas, the molecules only come into "contact", if you can call it that, when they happen to vibrate into one another. Thus the degree of vibrational energy that the gas molecules posess determines the aggregate "contact rate" for the molecules in the gas. The only way that a compression wave will propagate faster through such a medium is if the molecular "contact" rate is higher. The common name for the level of vibrational energy that the molecules of a substance have is : Temperature.