Quite likely, more complete responses to these questions would be found in some of the Stoic literature that has unfortunately been lost. But we do still have some more or less complete answers provided in some of the literature discussing and presenting Stoic doctrines. Anyone who wants to understand what Stoics actually taught and thought about the virtues can check out the discussions in Diogenes Laertes, Lives of the Philosophers, book 7 - which focuses entirely on the Stoic school - or in Arius Didymus' Epitome of Stoic Ethics.
Another excellent place to go is the works of Marcus Tullius Cicero, who - although not a Stoic himself - certainly viewed their moral philosophy in a positive light. He provides not only their views, but also many of their arguments, in work after work. One book that is particularly important for understanding how the Stoics came up with their four virtues is On Duties.
I taught book 1 of that work last semester, in my Ethics classes at Marquette University. As I typically do, I created some new core concept videos on key ideas from On Duties for my students. These below focus on the four virtues and how the Stoics derived a proper understanding of each of these virtues from consideration of basic features and impulses of human nature.
- Cicero On Nature and Reason
- Cicero on The Four Sources of the Right
- Cicero On Wisdom as the First Source of Duty
- Cicero On Justice as the Second Source of Duty
- Cicero on Courage as the Third Source of Duty
- Cicero on Temperance as the Fourth Source of Duty
You'll notice - as you read the early chapters of book 1 of On Duty - that Cicero and the Stoics aren't arbitrarily picking these four virtues out of a hat. Each of them is a main mode of distinctively human excellence, rooted in our common and complex human nature.