If he was married at the end of 2017, he would have to file Married Filing Separately,unless his ex was willing to file a joint return with him. 

If he was already divorced at the end of 2017, he'd file as Single.

If he was separated from his spouse for all or part of 2017, the custodial parent (the one the children lived with for the most days of the year) is the one who can claim the children. If he was not the custodial parent, he'd have to get a  Form 8332  signed by the custodial parent giving him the right to claim the child.