On the first part: See my other post for more, but basically, much (not all) of the homonymy is from older and/or written-only forms; and yes, ch and q don't sound any closer to a native Mandarin speaker than, say, sh and s do to a native English speaker or u and ou to a native French speaker.
On the second part: no defined measure that I know of. It would be a little tricky in that language is a moving target, everyone speaks it slightly differently, and even for a single speaker the "location" of a particular phone is more of a probability distribution even after you factor out varying context. That said, there definitely are charts that map out the space and take a stab at identifying the prototype location of each phone in the sound space, so it's not entirely implausible that you could summarise that with a distance measure. I strongly suspect that the value of the measure would not vary much among languages with similar-size phoneme inventories, though.
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On the first part: See my other post for more, but basically, much (not all) of the homonymy is from older and/or written-only forms; and yes, ch and q don't sound any closer to a native Mandarin speaker than, say, sh and s do to a native English speaker or u and ou to a native French speaker.
On the second part: no defined measure that I know of. It would be a little tricky in that language is a moving target, everyone speaks it slightly differently, and even for a single speaker the "location" of a particular phone is more of a probability distribution even after you factor out varying context. That said, there definitely are charts that map out the space and take a stab at identifying the prototype location of each phone in the sound space, so it's not entirely implausible that you could summarise that with a distance measure. I strongly suspect that the value of the measure would not vary much among languages with similar-size phoneme inventories, though.