One Parent Family Payment was known as the Lone Parent's allowance. It is one and the same payment.
Yes you can still receive payment if you are getting maintenance from the ex partner. How it effects your payment depends on whether you receive child maintenance, spousal maintenance or both. Your means are assessed and then this is taking into account when calculating your payment rate.
Note - if the child is part of a 50/50 access agreement, technically then lone parents payment is not due to either parent although it is hard to prove.