The answer is yes to both questions. NJ and PA do have a reciprocal agreement. If you are a PA (full-year) resident working in NJ, and NJ tax was withheld, then you file a NJ return with 0 income to receive a 100% refund of NJ tax withheld.
For PA, all of the income will be taxable. As long as the two lines associated with Box 16 on your W-2 divide your NJ and PA income, you will include both on your return. However if either of the two lines (NJ and PA) express at least the amount in box 1, then you will want to exclude the other line from taxes. Feel free to write back if this is the case, as there is a procedure to do this.
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