First question: correct. Both the state and NYC tax withholding are included on the NY State return. Second question: you do select NY. "None Selected" is if you are exclusively taxed in NYC, which is not the case. But the NYC tax truly needs to be factored out of the equation, because you should only be taxed in NYC for the period of time you were living in NYC. Once you moved to NJ, NYC no longer taxes you. To find this amount you will need to go back to the NY review screen, and see if there is a tax liability amount separated for NYC. If there is, subtract that amount from your total NY tax liability as well (the equation I gave you in my last comment), before multiplying by your NJ percentage.
However, if the NYC amount is not in the review, you can only estimate by multiplying your NYC tax withholding by 16.67%, which is approximately the correct amount. Use that number to subtract from your NYS adjusted tax liability, and then multiply by the NJ percentage. That will lower your NY tax somewhat but I don't think it will change your overall result. I believe you will still receive enough credit to bring your NJ tax down to zero.
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