Further, who has the final say on copy edits and type setting?
Short answer: everyone. In more detail:
Acceptance of a paper means that the editorial board approves it for publication. Once the editorial board signs off on the paper, some combination of the author(s), the editors and the publishers must arrive at a mutually agreeable final draft.
In my experience, the role that the editors play here is highly variable: sometimes they work directly with the authors on the copyediting: e.g. the American Mathematical Monthly is incredibly picky (relative to other math journals, anyway) about copyediting issues, and they surprised me by withholding final acceptance of a recent paper of mine until I had (myself, under their very specific instructions) completed all the copyediting and formatting. And they seemed serious about this: a change to the bibliography would be solicited and uploaded as a separate revision. It ought to be evident that I was not completely happy that the acceptance of the paper was held over my head during a discussion of the copyediting, but that's a way to play it and I'm sure they have their reasons.
(The MONTHLY has, I believe, by far the highest circulation of any mathematics journal. It is published by the Mathematical Association of America, which is the more teaching-oriented of the two professional societies for mathematics in the US. On the other hand, there are three selective MAA journals, and of these the MONTHLY is by far the most "serious". Long story short: many roads lead to them, and they are forced to be very selective indeed in what they publish, although they select for different things than a top research journal.)
I had another experience in which the final editorial acceptance in a prestigious journal was made conditional on the submission of a new draft containing less "pompous language".
More typically the copyediting and formatting is either left to the authors themselves or done by an employee of the publishing company (who in many cases does this for papers in multiple academic disciplines and thus cannot have high-level subject area knowledge most of the time). In the end both the authors and the publisher have the final say: both parties must approve the final draft in order for it to published, and the documentation of this mutual approval is the publication contract.
Of course in practice this mutual approval is done in an asymmetric way between the parties: the publisher sends you a form in which everything has been spelled out in advance, in the pushy manner of big corporations everywhere. But if there are clauses in the contract that the authors have a problem with, they are certainly entitled to ask, and in my experience some minor "concessions" (i.e., changes to the boilerplate agreement) are often made by the publisher. A big part of the asymmetry is that the authors generally have a much larger stake in the publication of the paper than the publisher does, so insisting that one be able to refer to a paper in the bibliography by [Cl14] rather than  or one will take one's wares elsewhere looks like a strange arrangement of priorities, but if you really do feel strongly about it you are entitled to ask and who knows -- maybe you'll get your way. Asking them to mess with aspects of the typesetting that are part of the journal's standard style seems less kosher to me: one would reasonably expect the journal to want to keep its standard style, and if this was really important to you, you should probably have brought it up earlier.
Making sure that one really does send in the copyright form last of all is a good tip. I stumbled on this point recently when dealing with one of the world's largest scientific publishing companies. They kept doing something weird in the proofs, I kept pointing out their mistakes and though I took pains to indicate in every correspondence that I was not giving my final approval, after a few go-rounds they didn't get back to me, and eventually I noticed that the paper was published online...still with one strange typesetting mistake that was not in the version I sent to them. Next time I'll save the copyright form until the end.