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.

No, only one parent may claim the child as a qualifying child to file as head of household.

• To file as head of household you must furnish over one-half of the cost of maintaining the household for you and a qualifying person. In general, only one of the parents will have contributed more than one-half of the cost of maintaining the household and be eligible to file as head of household.
• If a child is a qualifying child of both parents, there is a tiebreaker rule to determine which parent may claim the child. See Publication 501, Dependents, Standard Deduction and Filing Information for more information.

Generally, to qualify for head of household filing status, you must be able to claim a qualifying child or qualifying relative as a dependent. However, a custodial parent may be eligible to claim head of household filing status based on a child even if the custodial parent released a claim to exemption for the child. See Noncustodial parent is claiming our child as a dependent; do I still qualify as head of household?

You may still qualify for head of household filing status even though you aren't entitled to claim your child as a dependent, if you meet the following requirements:

1. You're not married, or you’re considered unmarried on the last day of the year.
2. You paid more than half of the cost of keeping up a home, that was your home and the main home of your child for more than one-half of the year.
3. Your child is your qualifying child for purposes other than claiming the child as a dependent and the child tax credit.

See Publication 501, Dependents, Standard Deduction and Filing Information for details.