My highly musical mother and brother seem to have simply memorized the relevant patterns, as you say.

Thinking along the lines of the in-progress Math Ability sequence, I think some people (including myself) are so reliant on being able to quickly derive and compute things in our heads that we have allowed our facility of memorization and memory-recall to atrophy. The prospect of learning, for example, all the individual notes on a guitar fretboard feels so agonizing to me that I still just "derive" the notes when I need them, even though this is terribly slow, after many years of playing the instrument.

As to Question D, a large fraction of scientists I've known are also musicians, so I think all we can surmise is that there are different ways that different brains can achieve the same objectives.