The temple description did seem to make it sound like a state-cult had formed around Seleukos, so it'd definately make sense that everyone claimed to be his descendant.I think i can answer the first question (at least before it gets confusing at the end of the empire): by birthright. All kings (with little exception) were descendants of Seleukos or claimed to be so and i think mostly the first born became the next king, although there were sometimes internal conflicts.
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