Not entirely true. If the air pressure and hence density is so low that gas molecules have little chance of hitting each other and hence passing on sound waves then the speed of sound is close to or at zero.
No, that does not affect the speed of sound at all, it affects how much the sound is *attenuated* over a given distance. At infinite attenuation (e.g. a vacuum) there is no sound at all and therefore its speed is meaningless.