What will happen with marriages? Which culture predominates? The male one?
Good point, in a marriage, I think people would retain their own culture, but could switch to the primary culture via events. The problem with children is again - static cultures.
If it is not through conquest and assimilation, how was culture changed in the Hellenistic period?
Cultural change was generally very slow and took place over centuries, and often was a two way street. Hellenic cultural prestige had many states adopt elements of their culture, such as styles of coinage, dress, elements of their urban culture, deities (even if it was just putting a Hellenic name on a non-Hellenic deity), cultic practices, names, and language.
Its a difficult question to answer, so I will just give some examples of non-conquest cultural changes:
Pontic Cappadocia Hellenised to a large degree (but also Iranianised a bit further) by its own volition, emulating both Greek and Iranian culture under the Mithradatids. Coinage in the Greek style was adopted, however these were not without Iranian influences either (a common theme also in places conquered by Alexander). Similarly, while many women were given Greek names, the entire male line kept Iranian names, and the same goes for many male relatives. The religiously the kingdom was a mix of Anatolian, Iranian, and later some Greek elements adopted voluntarily because it was, in essence, hip. The Greek language also seems to have become dominant amongst the elites at some point, yet when Strabo (a native) gives us the lay of the land, is clear that the average person in Pontus is still very much Cappadocian, and that the Tauric Cappadocians and Pontic Cappadocians in his mind (and he's personally been to Tauric Cappadocia as well) are the same people.
So even as the Iranianized elites Hellenized to some degree as well, the Pops were still Cappadocian. And what culture does that make the elites? Persian? Greek (what kind?) But on other levels they were still Anatolian as well, Pontus did not develop Greek style cities, its military had strong local elements (and even picked up the good old Scythed Chariots at one point!). And the state itself seems to have been quite Anatolian in its structure too.
In Pisidia on the other hand, voluntary Hellenization went all-out, however here towns (developing into cities along a Greek model over time). And while our knowledge of rural Pisidian culture is non-existent, the cities by the end of the game have almost entirely Hellenized to the point where its hard to not classify them as Greek, including language, customs, social systems, forms of rule, you name it. The Pisidians seemed to have been a very decentralized group, encompassing many tribal- and later city-states with territories of varying sizes, and super fond of their autonomy. Yet unlike many other cultures of Anatolia that had been in direct contact with Greeks for centuries (Carians, Lydians, Lycians, etc), and who also Hellenized more quickly after Alexander's conquest, but for whom the process had already been ongoing for a while, there is little to no evidence of any Pisidian-Hellenic interactions and thus nothing to speed up. (Though, part of the earlier interactions between Anatolians and Greeks was both ways, with especially the Carians, Phrygians, and Lydians leaving their marks on Greek culture too)
In game terms, they Hellenized completely, and not to Macedonian Greek culture, or the nearer Doric or Ionian cultures, but Aeolian, since the archaeology shows many elements we also see in Pergamon. Yet much of this seems to have happened
after the Attalid period, with only a few centres actively being Hellenized by the Pergamene kings. What seems to have happened is, due to the internal rivalry of the Pisidians, and the cultural prestige of Hellenism and in particular the Attalids (from the Pisidian p.o.v.) is that the other Pisidian cities were copying the original centres of Hellenic culture in an attempt to essentially out-Hellene one another.
And finally, the perhaps ultimate example of why culture needs work: the beloved Armenia. Which comes in 3 (or 4, but I'm not dealing with Commagene with its Anatolian-Armenian-Mesopotamian-Hellenic-Iranian culture) variations Lesser Armenia, Greater Armenia, and Sophene (still attached to Greater Armenia at the start, also sometimes called Lesser Armenia as well). Sophene seems to have Hellenised much faster then Greater Armenia (likely due to the closer contact with Hellenic cultures and the trade route flowing through it), even while it was part of it. With Greek culture in ascendance, to this part of Armenia it made sense to Hellenise to some degree because not just prestige, but also commerce (similarly, how many parts of Indonesia became Muslim, because it was convenient for trade, a new thing and became cool amongst the elites). Greater Armenia itself took much longer, and only really started to Hellenise when the Seleukids killed off its king, and even then it was still mixed with Iranian and Semitic elements and mostly second-hand. It was also very ineffective, and likely never left the elite sphere.
So within 1 state, amongst the same peoples (Iranianised Armenians), Hellenisation happens differently in different halves of the country. And other parts Iranianized further as well, because Iranian culture still held quite a lot of prestige in the region. And no Armenians, not even the elites, ever became something resembling Greek, during this time.
Yet in game, none of this nuance is present. Pops are either one culture, or another. Yet being part Hellenised seems to have had some extent of positive influence on Hellenic pops, as did being part Iranianised on Iranian pops. So what do I think could be done in game?
Without putting a lot of time in it, since it would require quite a bit of research to do well:
I've said this before, but I'd like to see a kind of cultural prestige/influence system. Build Judea into a mighty state, your culture (or culture group) starts to become more prestigious, which starts to keep the influence of other cultures in check. This starts to push your influence to nearby states as well, which eventually allows them to access bonuses related to your culture. On the other hand, their influence on you also gives you the option to select bonuses depending on the culture. You can do this actively, essetially embracing a foreign culture, which increases its influence, or keep it at bay, foregoing the bonuses but strengthening your own. Some of these things are currently present in the invention (and future tech tree) and this would be a good time to get rid off that terrible tech tree as well, though of course a lot of it is just deterministic nonsense in the first place.
Greek culture could for example come with things such as bonuses to legitimacy, city building, tolerance of other religions (interpretario graeca), and a focus on accepting cultures within your group, not outside of it. Persian cultural influence could grant bonuses that instead focus on multicultural empires though assimilation of Noble pops to your own, dynstical governors, food bonuses in deserts, mountains, and arid climates. Etcetera, with some elements being shared between culture groups where appropriate. Some of these
In turn, having certain levels of cultural influence either in your state or abroad can give some diplomatic bonuses, and in general things like names of characters, dress, etc, adjust accordingly. I'm a bit thought out on the subject for now, and have to get back to work, but in essence I think such a system could lead to not just interesting gameplay, but also replayability, while still being rooted in history.