Stoicism adopts a theory of oikeiosis, the root desire of all animals, human beings included, for self-preservation. An individual human being is, however, not only an animal but also a rational being. So self-preservation extends to preservation of oneself as a rational being; and this involves a correct attitude to things that are good, things that are bad, and things that are indifferent. The only things that are good are virtue and whatever pertains to virtue.
Our physical existence is counted as not bad but not good either - only indifferent. A rational being will put the full focus on acquiring, exercising and preserving virtue.
Since virtue involves interpersonal relations - the respect for justice between one another, for instance - human interdependence, if this means the recognition of others as moral subjects, is intrinsic to the Stoic condition.
You refer to duties. The Stoics do have a notion of duty but the emphasis is not on duties imposed on us, whether specific or general, but on the requirements of virtue which are voluntarily accepted.
However, the Stoics recognised three good emotions that were a proper part of a rational life :
▻ eupatheiai (joy)
▻ eulabeian (caution)
▻ boulesin (wishing)
These can fan out into benevolence and friendliness, modesty and reverence, good humour and cheerfulness.
The Stoics were notable for inculcating apatheia or freedom from passion. All interpretation is tricky but it is clear that this does not mean the cauterising of all emotion or there could be no good emotions. Apatheia more likely means (a) indifference to merely physical, non-rational existence as mentioned above) and freedom from a life held in the grip of bad emotion. The Stoics definitely recognised bad emotions, among them :
▻ phobos (fear)
▻ epithumia (greed)
▻ lupe (grief)
I am not sure how far this account of Stoicism answers your question or how far an answer to your question can be derived from it. Perhaps it will rotate your perspective on your question. I am not sure that from a general view of Stoicism your specific queries can be directly answered. I have offered what I can.
John Sellars, 'Stoicism', Chesham : UK : Acumen Publishing, 2006, ch. 5 'Stoic ethics', pp. 107-134.
E.V. Arnold, 'Roman Stoicism', London : Routledge & Kegan Paul, 1911/1958, ch. XIII & XIV, pp. 301-356.