No, you may not file as head of household because your spouse lived in your home during the last 6 months of the year. You are married for the whole year if you are separated but you haven’t obtained a final decree of divorce or separate maintenance by the last day of your tax year. See Publication 504, Divorced or Separated Individuals for more details. 

Your filing status for the year will be either married filing separately or married filing jointly.

You cannot claim the credit for childcare expenses or the earned income tax credit because these credits require married taxpayers to file a joint return to be eligible for the credit. You may be eligible to claim these credits if you decide to file a joint return with your spouse.

• Some taxpayers using the married filing separately filing status can be treated as not married to claim the earned income tax credit or the credit for childcare expenses. To qualify, the spouse claiming the credits cannot file jointly with the other spouse, needs to satisfy certain other requirements (for example, not have the same principal residence as the other spouse for the last six months of the year, or are legally separated according to state law with a written separation agreement and didn’t live in the same household as the spouse at the end of the year), and must have a qualifying child living with them for more than half the year. See “Special rule for separated spouses” in Publication 596, Earned Income Credit (EIC). 

See What is my filing status? and Publication 501, Dependents, Standard Deduction and Filing Information for information about filing status.