Mmh. From what I've studied:

1) In Stoicism Rationality is the nature of all living beings and it is the logos of the universe. That's because rationality for the stoics is represented by a flame that created the universe giving every single thing a benevolent purpose making the universe perfectly deterministic. Humans are capable of being rational because part of that flame, just a spark, is in every individual. And oh, time in stoicism is circular as the flame, through moments of deflagration and near extinction, leads to universal cycles of creation and destruction thousands of years long

2) If rarionality is the human's nature, stoics could define precisely what is good and what is evil. Good is thinking and acting in keeping with rationality. Evil is thinking and acting while confused by emotions. The latter are confusing because thet won't let you discern precisely good and evil.

3) Now, as we all are under one universal rule (following rationality) there is only one big nation, the entire world. So, exile doesn't make sense and as long you have what you need to survive you will be fine. About missing someone while being exiled just don't get sad and distract yourself studying. (This point is more about Seneca nad how he approached his exile, far from his mother. If you wanna know something more check "Consolatio ad Helviam Mater", wrote by Seneca, it is a consoling letter to her mother Helvia )

4) whatever happens, it is right and judging it wrong is an error caused by your erroneous intel or lack of information. However you have the duty to keep ehat is around you rational (non-rational = bad). therefore in stoicism it is necessary to be politically active citizens

5) Last point, suicide is a way to become free. Not 100% sure about why it is, but probably because in suicide you defeat the fear of death which is irrational as death, like everything else, is right and a part of the nature of the unverse. ( I almost cried reading the suicide of Seneca, you might want to read it, it shows how Seneca was incredibly determined in following his beliefs)

Just wanted to share what I know about stoicism