There is no "divorced" filing status. Your filing status is based on your marital status as of December 31st of the tax year. If you were divorced as of that date, you can file as Single, or (if you're providing a home for a dependent) as Head of Household.
The right to claim a child as a dependent belongs to the custodial parent. The IRS considers the custodial parent to be the one with whom the child spent the greater number of nights during the tax year. The non-custodial parent cannot claim the child without a written release (IRS Form 8332) from the custodial parent.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.