What are the duties and responsibilities of single parents?

Answer 1

There are very possibly societies where duties are owed by a family, but Western society of today is not one of them. A family is not considered a unit which owes duties or gets rewards, only the individuals in it. In particular, in our society, we do not have a concept of "filial duty" owed by children to their parents, only "parental duties" owed by parents to their children, and these duties are the same, no matter how many parents a child has (with divorce and step-parents, it could be as many as four): the parent has the duty to feed and clothe the child, to provide for his or her every want, to provide educational opportunities, and supervised recreation, and to keep the child safe from every possible situation where he or she might be harmed or hurt.

Answer 2

Exactly the same as all parents. Being a single parent does not add or remove parental duties.