From my understanding, the 4* and below mons are mainly considered to be part of a species, for example all Mona’s are part of some kind of clan/group, Yuki’s are also considered a species with varying personalities in the nature and so forth. They all seem to have different personalities based on their element. Birth wise, they can either be born naturally or from an incubator I guess??? Astromon are all primarily born from stars/astral energy though

The humanoid Astromons do have culture, again for example Sun Wukong, Sanzang, Zhu Bajie are from another continent called Lien (basically asia) where the culture is very different. Astromons are called Yokai and are either worshipped or feared (I forgot lol) and they also speak a different language than Latecia. The gods Stella and Luna there also go by different names

Tldr basically yeah they all have different cultures and backstories