Yes. The IT-182 will hold the loss.
1. IT-182 does require a federal PAL be recomputed based on your NY modified AGI. Your entire $5,000 NY loss is allowed for NY purposes.
2. Yes, you will have a negative income and allow any NY tax withheld on the RSU to be refunded to you.
3. The $2,000 loss is a net operating loss. You can carry it forward to offset future income.
Reference: NY Nonresident
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