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I am writing a book that is set in England, but because I would get the book published in America I don't know what terminology to use. My main character is in the equivalent of 7th grade but in England they would call it Year 8, which might be confusing to my directed audience. Should I stick with American terminology or use English ones?

If you're writing for an American audience, with an American publisher, then use an American dialect for your narration.

But... your character is living in England. Whether she's British or an immigrant or a visitor, she's going to be exposed to the local dialect. She will use local terms when appropriate. If she's in Year 8 in school, she'll say that. She might translate it for her friends and family in the United States, but she wouldn't say "7th grade" when talking to other people at school or in the community.

Your narrator may also do some translation, depending on the audience. If the entire book is simply set in a foreign country you would use local terms but translate prose to American English when appropriate. The only difference between this and a book by an American author that's set in China, for example, is that both countries here speak the same language.

The dialogue in your story will be whatever it would be in real life. If your main character is English then her dialogue will be too. If she's American, she'll probably code switch, meaning she'll use different dialects with different listeners. And even her American speech will be peppered with some local terms. Her year in school will definitely be whatever it's called. Just like an American graduate student in English will talk about their MPhil program but might say "masters program" for people back home, even though they're not quite the same.

The other issue you have is translation. Some Britishisms aren't immediately obvious to Americans (MPhil being one of them). So use context so your readers can figure it out (at least get the gist when it's a term that isn't vital to know) or show your character explaining the terms to an American listener (don't overdo this, it gets tedious). Be aware of what your American audience won't know (use beta readers for this) and tweak it.