Never thought about it, but yes, probably.

Either that, or the quality of the noise reduction reduces. Imagine again playing a sound with throughs where the original sound had peaks and visa versa, but with a smaller magnitude than the original sound. Now the magnitude of the resulting wave will still be reduced, but not become exactly 0, so the noise cancellation will be imperfect

In particularly hectic environments, my AP Pros struggle to really block a lot of noise, mostly just voices and car sounds, but larger noises still make it through the headphone itself, bypassing the mic (but also hitting the mic, so you get some amount of ANC on it) and hitting your ear.

I think this would be a similar question to asking "do my headphones die faster if I listen to things louder", which I don't think is a big enough effect to worry people, I've never heard of it anyways. There's pretty much never not sound. Surely headphones have a lower level of reception or tolerance where it doesn't bother or can't pick up those noises, but it would always need to be listening and ready to generate them, so whether it does and how much it does seems like it'd be the smaller part of the process

Yes it only considers the combined total mix, not each individual source. All it can do is measure the soundwave that actually reaches your ear, using a built in microphone.

Think of being in a pool. You've got 4 different people swimming, splashing, diving in - making different sizes and types of waves at different locations. But that doesn't really matter - you're at one end of the pool with a little float that bobs up and down and traces the net combined total of all these waves as their combined peaks and troughs reach you.

That little float is like the microphone in noise-cancelling headphones. The microphone measures the total net combined sound wave peaks and troughs reaching your ear, and then the headphones play an "opposite sound" that has peaks where the room noise has throughs and troughs where the room noise has peaks. The peaks and troughs cancel, and the room noise is imperfectly but substantially eliminated.

And yes it's an engineering marvel that this measurement and active response can happen at the speed of sound in an ear-sized device.

think of waves in a bathtub or pool, or even an ocean. the waves are highly complex, and you may not be able to cancel them all perfectly, but if you can just knock down the peaks and troughs, you'll make things much smoother.

Throw in some white noise and you can drown out the rest.

It doesn't detect them as multiple frequencies until later, it just samples the incoming sounds and creates a digital version of the analog measurements. from the mic.

There's a thing called 'digital signal processing' which then can then analyze the digital signal and break it up into it's composite frequencies/magnitudes, average out the noise. The way the processing is handled will determine the quality of the end result.

Some cool things to learn about would in Nyquist Theorem, Fast Fourier Analysis, and Digital Signal Processing (FFT is part of this but deserves it's own mention).

For it to be effective the waves need to line up and be in sync. You can't know where a sound is coming from, but you do know where it goes. Right into the ear. So you cancel it there.