Ok, today I'll try to focus solely on the topic of dwarven culture. My idea of how it should be organized is a quite complicated one, but bare with me, as I hope you'll find it rewarding.
As I've already stated the dwarven society is a matriarchal one due to the small number of females. No one knows why the number of females being born is significantly smaller from the number of males, but it should be obvious that this long lasting phenomenon has led to a society in which women are highly privileged.
Here are some ideas I have about their society:
The society is organized into clans, which follow the rule of matrilineality , meaning that the lineage is established through the mother and maternal ancestors.
Dwarves cultivate polyandry. That is, one woman may take many husbands (in this case the maximum is 3), each of them however has to pay a dowry (or a lobolo if you prefer) before he is accepted as a husband.
The tradition has it, that such a fee must be payed only in what a male can carry by himself (counting what he wears). This might have given a beginning to the strange concept of dwarven money, which are shaped into spheres of gold, silver or copper, that are worn on display by being thread into beards, or worn as necklaces.
Dwarves are also avuncular. This means that a child is brought up not by it's father but maternal uncle. There are several reasons for that, the main one being to secure that all fathers will treat the child equally well (which of course doesn't work so well in real life) and to create a stronger bond with the clan, than with the family.
To avoid incest, dwarves are forbidden to marry into their own clan. This rule also secures the strong connection between the clans.
There exists a dwarven king, however his role is mainly representative. He is the leader of the Council of Clans, which appropriately to it's name consists of all the clan leaders (or their representatives, each of the clan leaders can bring all her husbands to join the discussion) with each of the council members, including the king, having one vote. The king also holds the title of the First Warrior. It means that in case of an armed threat to the dwarven kingdom, he becomes the leader of the armed forces, since the counsel has no word in matters of war.
The last thing is the problem of half-dwarves. It's obvious that my previous idea for that race doesn't fit this concept. Thus I need to turn it around a bit. Indeed half-dwarves aren't shunned by dwarven society, however as they can't participate in the reproductive cycle, their social status is rather low. Marrying outside the race is not forbidden, but it carries some social disadvantages, as the dwarf marrying a non-dwarf looses the privilege of being able to use the clan vaults and has to raise their child on their own.
not yet! I wanted to say one more thing that I forgot to add. The slavic and nordic dwarfs stay, simply some clans lean one way and some the other. Is based on geographical location. That's all!