No, IRS will not question why those boxes are blank. Boxes 16-20 are state and local tax boxes. They have no impact on your federal tax return unless there is withholding in Boxes 17 (state tax) or 19 (local tax).
New Hampshire has no income tax and there is no state or local tax withheld, so leaving those boxes blank will not affect your daughter's federal tax return or draw attention from the IRS.
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