It is possible to get a very small amount of power from phone audio jack. You need to set up a bridge rectifier to turn the AC audio signal into a DC voltage, then use that voltage to charge a capacitor that will in turn power your circuit.
Total amount of power you can distil from the audio output depends on a lot of factors like...
- What voltage you need
- Are you willing to add the complexity of a buck/boot converter to your design
- What device is driving the audio (for example, some phones have lower maximum output levels than others)
- What signal are you going to send out the audio (are you going to be able to generate a sine wave, or are you stuck with the Daft Punk the person happens to be playing?)
- Are you willing to add circuitry to rectify both sides of the stereo signal?
A good estimate is that you should be able to pull on the order of about a milliamp. Just enough to maybe power an MCU that is mostly sleeping and an LCD display, or rarely blink an LED or make a sound.
It is possible to do bidirectional data transfer over an phone audio jack. Probably the simplest way is to send tones in each direction.
If you add more about what you are trying to do, I can give more specific details.