Yes.

It depends. If there is one child, then the answer is no. If there are two children and you share equal parenting time, then you can agree that one parent has one child 183 days out of the year (one more than half) and the other parent has the other child for that amount of time.  That way, you can both qualify for head of household.

Yes, if your child lived in your home for more than half of the year, you may file as head of household, even if the divorce or separation agreement gives your ex the right to claim the dependency credits.

The requirement for a qualifying child or dependent extends beyond just your own son or daughter. To be considered a qualifying child, the child must meet the criteria in each of the following categories:

1. The child must be your biological or adopted child, stepchild, foster child, sibling, step sibling, half sibling, or a descendant (child, grandchild, great grandchild, etc.) of one of these relatives.
2. The child must have lived within your home for more than six months during the tax year.
3. The child needs to be younger than you.
4. As of the end of the tax year, the child must be under 19 if he is not a student, or under 24 if he is a full-time college student.
5. The child must not have paid for more than half of his living expenses during the tax year.