could you then email our New York office with the sales figures for this month?
It's part of a conversation but I've written this just for example. Why must we say "New York Office" rather than "New York's office"?
When is it possible to use Possessive Case, when could we use a format like "New York office", and what do you call that?
New York doesn't possess anything in this sentence. It is being used as an adjective to qualify "office." That's all.
To be frank, I'm not really sure what you're asking with your other questions. You can use "New York office" whenever you want to describe an office that's in New York. A valid usage of "New York's" might be something like:
It's a very tall building, but not as tall as New York's Empire State.
The Empire State building is a cultural icon strongly associated with New York, so although New York as a city (or a state, depending on context) cannot "own" things, the building "belongs" to New York. It is a bit of a metaphor in this usage.
Other things that you can apply possession of a place like New York to would be: its laws, history, officials, etc.
