Yes, all income is included and taxed to New York (NY).
Yes, include the income on California (CA) earned during the residency and then claim a tax credit for the tax you paid to NY on the same income. This will require some calculation on your part. You can take the full income, then divide it by the amount you are claiming in CA. Once you have that percentage you can multiply that by the amount of tax liability for NY. This will be the credit you are allowed on the CA return.
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