What does the typesetting process for a math/science journal using LaTeX look like? Hopefully this question isn't too broad. Following up on https://tex.stackexchange.com/questions/99123/what-software-do-publishers-use and Elsevier production team messed up my paper. What should I do?, what is the overall process that a typical academic journal uses for typesetting a LaTeX document? I would appreciate a brief step-by-step overview of the process.

Some random questions that I've often wondered about (no need to answer them all): does each journal just have a LaTeX template with a really elaborate preamble, into which they mostly copy and paste the TeX submission and then make minor tweaks from there by hand? Can it possibly really be true that Elsevier usually retypes the entire article by hand, as an answer to the linked question above claims? That seems completely ridiculous. Do the typesetters have any math training at all, or when they typeset equations, are they just manipulating symbols in what is to them effectively a foreign language? Is there at least someone around who understands the paper to whom they can ask questions if they're not sure how an equation should be formatted? Is it true that they're almost always in India?

I would especially hope that during the proof revision stage, there's someone around who understands the paper content, because understanding an error in an equation can be nontrivial. If one were to write a comment on an unrevised proof like, "These parentheses are misplaced; they should group the Jacobian determinant together with the integration measure", would anyone on the other end be able to understand that comment?
This may differ quite a bit from journal to journal. In the best of worlds (from the author's point of view), the LaTeX source is used in some robust automated process to generate the final product, e.g. using latex or pdflatex, possibly with a slightly different documentclass and different fonts.

However, often the paper is typeset using a completely different "professional" typesetting system, for which there may be an automatic conversion from LaTeX. It may well be the case that many equations have to be corrected or completely typeset by humans. In this case, the person in charge will most likely have no training in mathematics, but they just manipulate symbols in what is to them effectively a foreign language. However, they should be able to understand LaTeX.

If the proofs are hopelessly messed up, then don't even try to correct them, but send them back demanding that the paper be properly typeset according to your LaTeX source. Point out roughly what the errors are and how many. It is the responsibility of the typesetter to set your paper properly and according to the LaTeX source.