Why are high impedance circuits being more sensitive to the noise? They have less current flowing through them, but how is that related to noise, since external noise becomes voltage on the wires, and then current proportional to resistance?
You can model a capacitive coupling between a noise source and your circuit with 3 elements :
- a voltage source (the noise source)
- a capacitor (the capacitive coupling)
- a resistor (the input impedance of your circuit)
If the resistor has a small value, you won't get much voltage at the input of your circuit If the resistor has a big value (high impedance), the voltage will be much higher.
When you start speaking about noise the subject becomes quite complex. Because noise must be defined, which is not that simple. A signal (meaningful information) in an electronic system A could be considered as a noise in an electronic system B. I could give an example where a low impedance input is more sensitive to noise than a high impedance one, it depends what you consider being noise and what you consider being signal.
I see in your question that you might be a bit confused with DC and AC... Ohm's law is basically a DC law, and can be extended to AC when replacing the resistance by impedance, like below:
When you use the term impedance you implicitly consider AC signals. I suggest you to read the wikipedia page about the electrical impedance.