In common, "by" means "bằng" , "in" means "trong" (inside of space), but:
"By" means "bằng" when it is used for showing how or in what something is done.
Ex: The house is heated by gas.
But, in this case, we are talking about how to say some words in a language, so we have to use "in" also means "bằng" to show the language
Ex: How to say "Xin lỗi" in English = "Xin lỗi" nói bằng tiếng Anh như thế nào?
I think that "using" would be a more clear, additional translation. That word can be used in all/most example sentences, although sometimes it would be unnatural. But, for making the meaning clear, I think it helps.
The house is heated using gas. I go by foot (using my feet). Say "xin lỗi" using English.