Yes, you would consider only the SC tax on the portion of wages that was earned while living in NC. The tax on the SC return for the wage portion you earned during the NC residency period. Without the interest and dividends you can use the formula to arrive at the correct SC tax imposed on your NC residency period.
So to be clear, you do have a part year residency in SC and you must pay tax on wages earned during that period to SC. Those wages should have no affect on the part year residency in NC.
Yes, once you have that calculated (use the formula from the previous answer) and enter the appropriate wages and tax paid on SC for the NC residency period. Your question number 2 is exactly right.
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