When you say income greater than my exemption, what exactly do you mean?
I definitely dom't have the equivalent of $10,000 anywhere so that's no problem.
As for NY state, I know you can break residency from it if you are living outside the state for a certain amount of time. This makes it so that you legally won't have to pay taxes in the state. I learned this a few years ago on here actually. I've never done it as my state taxes were never that high.
I just know that in the past if I've not worked when I've lived in the US, I don't fill out the tax forms as there is nothing to fill out. This only happened once I think and since the same happened this year I wasn't sure