The free market is more than capable of handling those duties you slavishly think govt only can do.
Pity you have more faith in government than God or free enterprise.
You are correct except on parental authority, and you left out:
Wrong. They believe children can emancipate at any time. That negates parental authority.
However, children always have the right to establish their maturity by assuming administration and protection of their own rights, ending dependency upon their parents or other guardians, and assuming all responsibilities of adulthood.