As with most things, it is largely a matter of practice and experience. There was a time when I was fast enough to take lecture notes in LaTeX, in courses where there were many formulas to be typeset. I did get an odd look from a professor one time, where at the end of a one-hour open-everything exam, I turned in a typeset pdf rather than handwritten answers.
Sadly, I am not as proficient with it as I used to be, as it has way too much esoterica in getting the exact layouts you want.
That depends on the field and the specific publisher. Since the turn of the millennium some scholarly presses have stopped accepting LaTeX; this is often related to outsourcing typesetting to Indian shops that are not LaTeX-savvy.
It's like an ancient secret order that is keeping the world safe from word-processors.
I have no idea of what they do, or how they do it, but I can't argue with the world-class results.