Cicero and Natural Rights

Cicero writings show us that he had studied Aristotle, Polybius, and Zeno of Citium. Cicero also gave us one of the first clear statements of Natural Law theory. But his texts also present us with some questions:

Was Cicero a stoic, or did he merely report stoic ideas?
What, exactly, is stoicism?
Did stoicism have any significant influence in Roman society, or is it simply frequently mentioned?

Understanding the difference between discovered objective Natural Law and legislated subjective Civil Law, and the accompanying difference between Civil Rights of Citizens and Natural Rights of all humans, will be the key to understanding the lasting influence of Natural Law Theory, including the present day.