You were a part-year resident of NY and moved to PA, again as a part-year resident. You worked in NY the entire time.
For the amount owed in PA you should select option 3.) "I need to make an adjustment to the taxable amount of income"... then adjust proportionally for the amount I earned while living in PA, then claim the tax credits paid to NY.
For your second question, you will pay tax in NY for 100% of your income because you worked there. You will report the proportional amount in PA for the time you lived there. You'll then get a credit for taxes paid in NY for that proportional amount.
If you have income other than your wages from this job that are not taxed, it will be taxed in PA. If this is a significant amount you may choose to pay estimated taxes to PA. You do not have to pay PA estimated taxes on the income you earned in NY.
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