Yes, prepare your non-resident tax return first (New York), determine what, if any, taxes are owed to NY, and then when you prepare your California return, you can claim whatever credit is available for having paid tax to NY.
No, as to your second question, as it appears your allocation is not balanced. The majority of your mortgage interest should be allocated to CA. In the NY section of TurboTax, after the screen that relates to NY additions and subtractions, you should see the screen, Your mortgage interest and points deduction. Perhaps you have already seen this screen, but it is here where you can allocate to NY, that portion of your mortgage interest reported on your federal return. From your post, maybe that $20,000 amount was already entered in the NY field. However, you need to adjust the amount being allocated to NY to reflect your period of non-residency while you were earning income from a NY source.
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