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In general, the short answer is simply 'no'. Cutting out an instrument entirely in the mastering stage of a recording, is completely impossible. Even if you are having balancing problems that are not due to frequency ranges in your listening equipment, it is hard to believe that the balance was good when you were actually mixing it down. This is a problem ...

The "cocktail party problem" is actually a famous example in signal processing, and there are several different Blind signal separation or Source separation algorithms to solve it in different conditions. Are you doing this for homework in such a class? I've got an example of one on my website, but this statistical method (ICA) wouldn't work well for you ...

You cannot solve for x and y in the equation: x + y = 5 because you do not have enough information. If you knew what x was, you could find y, and you can find what x and y are in relation to each other (e.g. x=5-y), but you cannot find both values without more info. Likewise, once two signals are mixed, you cannot find what either sounds like by itself ...

I think you may be misunderstanding the usual split, which is between low and high pitched sounds. The bass speakers play the low notes and the tweeters play the high ones. Loud is not opposite to deep. You can have loud low or high notes, or quiet low or high notes. To answer your identification question - low pitched notes will have only a few waves, ...

(I submitted this answer to the SO version of this question, I assume one or the other will be closed, not trying to pad rep or anything) You might look into the LMS algorithm by Widrow and Hoff. You could apply it to each of your mixed recordings, using man.wav as the desired reference and woman.wav as the disturbance signal. There's also a way to use it ...