Yes, based on the information provided your daughter is a qualifying child for purposes of the EITC. See this IRS Publication 5334 Step Two for the eligibility requirements for a child.
No, you cannot file as head of household, because your daughter doesn't meet the tests for a qualifying child or a qualifying relative. She provided more than half her support for the year. See IRS Publication 501, Table 5 for the dependent qualifications.
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