you should not say you are british but a futur yankee!
This is a bit dangerous. If you do not say you are British, what do you say you are? If you claim to be a US citizen when you are not you break the law in a big way. If you look on the US citizenship application form they specifically ask whether you have pretended to be a US citizen. (Together with some far more ridiculous questions, but I digress).
If you are a green card holder, you need to tell them that you intend to permanently reside in the United States. That's all. You don't need to tell them you intend to become an American because they don't care about that until you apply. Keep your mouth shut unless spoken to, don't get clever, pay your taxes on time, and don't lie.
As for the rest, I'm not sure what you are talking about there either.