Yes to both questions, as long as you're both in agreement. Either of you can claim your daughter if you both are living with her. However, if both were to try to claim her at the same time, the IRS would side with the parent who either lived with her the longest (first), or, if the same amount of time, which parent had the higher income. But as long as both parents lived together and only one claims your daughter, this is okay.
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