Yes for HOH, if 1) you are unmarried; 2) you paid more than 50% of the cost of keeping up the main home; AND 3) if a qualifying person (read: Your daughter) lived with you for more than half the year. If you cannot claim the exemption due to a court declaration, you can claim HOH without claiming the child' exemption.

Yes, for EIC. By IRS rules (rule 9 for EIC, IRS Publ 596(see examples)), only the CUSTODIAL parent is able to claim the following: HOH filing status, child/dependent care expenses credit, income exclusion for dependent care benefits, and the EIC. If there is not a court decree, the IRS has determined that the custodial parent is the parent with whom the child lived with for more than half the year. Based on the information you gave me, only YOU can claim the EIC, HOH filing status, and the other credits. If there is a court decree stating the NONCUSTODIAL parent can claim the child's exemption, then the father can only claim the child's Exemption, and the Child Tax Credit. You are only able to claim the other benefits.