A - I can transpose at sight, but not very quickly. Like grouchymusicologist, I do it using the concept of scale degrees.

B - I suppose it is plausible. But I can't think of any real-life examples. Learning good posture isn't going to hurt any athletic skill you try to develop. Having studied linguistics is only going to help you when you start to learn <random obscure language>.

C - I've never heard of such. Natural systems tend to be pretty intuitive.

D - Artists are the people who understand that what's on the page isn't music. It's just instructions on how to play the music. Theorists are the people who develop the notation, and they have a lot in common with scientists. (Many musicians are both.) Yes, some aspects of music notation and theory are counterintuitive. So are some aspects of mathematics. Plenty of people can do both with a high degree of skill.

Other than that, I don't really know what to tell you - except to use your highly trained mind to come up with ways to practice doing the things that you have problems doing, until you can do them well enough to please yourself.