C-1 is correct regarding an allocation of income between grant date and date of vesting.
For C2, the regulations state that the allocation period ends the earliest of when the stock fully vests, the stock is sold, or your employment terminates. It is not clear whether termination would equate to your reassignment to another state. So, I'm not sure you are correct in assuming there would be no New York income when the stock vests if you are no longer a New York resident, because you still work for the company.
C-3 is correct, you are taxed by New York State when working there, but New York City would not tax you unless you were a resident.
C-4 is mostly correct. The investment income your earned while a resident of New York is New York income versus income earned elsewhere, and you use that ratio to determine how much of your New York tax you have to pay.
You can read this from the New York State Department of Taxation and Finance to learn more.
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