1. Yes you can claim her as a dependent if she was under 24 and a full-time student since she did not provide more than half of her own expenses and she lived with you more than six months during the year.
2. Her residency would be Part-Year Pennsylvania and Part-Year Idaho.
3. She will have to file for PY PA (1st and 2nd W2) and Idaho (1st W2 as nonresident, 3rd W2 as resident)- prepare the ID return first because she can can claim a credit for the taxes paid on the 1st W2 as NR to ID.
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