In what age range and development area do individuals test the rules and limits of authority figures? age range? type answer here. development area? type answer here.

10 -13 years and "formal operation" stage of child development

Explanation:

Generally, children are tested upon by authority of their parents at the age of 8 to 9 years and by the age of adolescent i.e between the age of 10-13 they are completely under the influence of authoritative  figure of their parents.

Children between the age of 10 -13 years are in "school age" group and come under the "formal operation" stage of child development.