My first inclination when thinking about the Cocktail Party Problem would be to use adaptive beamforming to isolate different signals, but this does not seem to be how the problem is commonly thought about. Indeed, basic ICA assumes the signals all arrive at the sensor array at the same time (instantaneous mixing), and breaks down when there are significant delays (see this question for example).
So what is the relationship between these two approaches? Could they be combined in some way? I know there may not be a definitive answer to this right now, so partial answers/insights are welcome.
Second question: What defines a delay that is too big for ICA to handle? Is it relative to the sample rate, or the wavelength?
Edit for question 2
I assume ICA will break for a delay of $\lambda /2$ ($\lambda$ is the wavelength), but will ICA work for delays significantly less than that, or is a 1 sample delay between two sensors enough to foil ICA? How brittle is it?