1: When he listened patiently, although he did not want to be there. (The noun is father, father is a masculine noun, therefore you use masculine pronouns)
2: They played first. Most of them were prepared.(The noun is youngest children, youngest children is a plural noun, therefore you use plural pronouns)
3: when she played, her playing was sloppy.(The noun is daughter, daughter is a feminine noun, therefore you use feminine pronouns)