This doesn't directly answer your questions, but I can share one example where our sensitivity to phase information becomes apparent: when you play the sound of a pair of hands clapping. It's a great test case for hearing when a set of speakers has phase alignment problems, which is underappreciated as a metric for speaker systems. (It's rare even for experts to put a lot of effort into uniform phase response when designing speakers. It's one of the hardest things to manage. Frequency response, harmonic distortion levels, dispersion and even aesthetics usually take priority.)
Likewise, if you mess with the phase alignment of different frequencies in a hand clap sample and play it through an otherwise phase-coherent source like ear buds or headphones, the misalignment is really obvious.