(not a teacher)
1) You should use "on". Also, there should be an article (a, an, the) in front of "server". It's understandable and grammatical, though the verbage is a tad stiff, if that makes any sense.
2) The bolded phrase makes no sense. Perhaps you could say "....she would reheat it for me." or "....she would exchange it for a hot one for me." or "....she would send it back to the kitchen/cook." This all depends on the type of dish we're talking about.
3) Not really. I'd say something more along these lines: "The server told me she would take it back to the kitchen and have it remade without onion." or "The server told me she would have the cook prepare a new dish without onion."
4) You could use either one. Note that "instruction/specification" should be plural here.
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