Yes, there is nothing to prevent her from receiving child support despite any past agreement. However, it sounds like there is a lot going on that might affect the child support calculation. I would definitely speak with an attorney to make sure the support is calculated correctly. Specifically, there may be an argument for imputing income depending on the reasons she was fired, he needs to make sure he gets credit for the health insurance, and, if he has more parenting time than the standard order in the county that granted the divorce, don't forget to ask for a downward deviation due to increased parenting time. He will likely be on the hook for child support, but there are things in the facts you presented that may mitigate the amount. Good luck!
Yes, they are his children and she can ask for child support even years after the divorce.
This information is intended as general information only. This communication does not establish an attorney-client relationship between me and the asker.