1. Is there another way to show that this money was used for moving expenses? Or does it not matter because I don’t meet the distance requirement and that money reported in box 12 is taxable?
It doesn't matter if you don't meet the distance test (please check again). Tell your employer as he may have taken a deduction that he shouldn't have and instead should have included it in Box 1 of your W-2. He would have chipped in on the payroll tax if that were the case. Also, ask if there was or could now be some "gross-up" to cover for your now increased tax bill.
