COUNT or PULSIN could be used to determine the frequency of an input but it would only work well for pure tones and very clean signals. Most sound isn't a pure tone so I doubt whatever you want will be achievable with a PICAXE ( or many other micros for that matter ).
Playback is another issue. PWMOUT can generate a signal of a certain frequency, but only a square wave.
You'll need to describe your application in greater detail for more precise answers. Is amplitude important, is it a point-sample of frequency or a continuous, changing frequency you need to handle ? What is tha source of the sound, what frequencies ?