ire Nation culture:
There is no fire lord. The monarchy does not exist and doesn't exist for thousands of years. Fire bending is a trait that elevates bloodlines in the hierarchy of their society. The fire nation comprises of a ton of islands and each island governs themselves. They partake in tribal warfare as well, but that's beside the point. The familial hierarchy of the fire islands is tier based. If a bloodline possesses the ability to fire bend they are most likely to be nobles, governed by the strongest and most resilient of the families on each island. Nonbenders would be the "peasants" in this tier based culture. When a child is born with fire bending abilities they elevate the family's status, and they are trained from the youngest possible age to hone their bending skills, further elevating the family's status. Agne Kai can be utilized to challenge the ruler of the ruling family to reorganize the power structure on an island to island basis. Failing to meet family's expectations can lead to disgrace, not only for the individual, but for the family as a whole, because families as a whole are also held to certain standards and expectations as well depending on the tier they possess within their culture. Great deeds and achievements, feats of notable regard, etc. also elevate family.
Earth Dynasties:
The Earth Kingdom will not exist for thousands of years either. This giant landmass is divided into several dynasties, of which also partake in tribal warfare. These dynasties are ruled by those chosen by each territory's respective spirit. The divine right to rule is passed down via bloodline until either the bloodline is wiped out or the territory's spirit selects a new ruler. These rulers are worshiped as gods by their people and they demand unyielding loyalty from their subjects. How they choose to govern their dynasty is completely up to them, however, the spirits can intervene however they see fit, removing them from power. Nobody knows what reasons the spirits might have for doing this yet as spirits are immortal and humanity has only gone a few hundred years without the lion turtles protecting them.
Water Tribes:
The people of the water tribes are very community oriented, and unlike the fire islands and earth dynasties, the water tribes do not partake in tribal warfare. There are no rulers within the water tribes either, but instead, it is every water tribe citizen's duty to provide wisdom and conflict resolution as they become the tribe's elders. The elders of the water tribes are deeply respected and regarded as arguably the most important people in the water tribes. Regardless if someone can bend or not, every citizen is viewed with equal importance and treated with equal dignity, and are trained to do their part for their tribe to the best of their abilities, whatever that might look like on and individual to individual basis. However, those who do not pull their weight, or those who repeatedly burden the efficiency of community, are often exiled for a period of time and able to return once they are able to prove their worth after living in the wilderness of the tundra alone, if they survive. Despite their station or occupation, all water tribe men are trained as warriors and fishermen as it isn't uncommon for people of other nations to attack them, believing them to be weak. The Northern Water Tribe is the heart of both water tribe's spirituality and philosophy, whereas the Southern Water Tribe acts as the tribe's wisdom and worldliness, as it is far more common for southern water tribe to venture to the north pole than it is for anyone in the north to venture to the south. Every few years people from the southern water tribe trek to the northern water tribe and a festival to celebrate their travels and arrival takes place, where the two tribes will exchange knowledge and teachings, stories, wisdom, goods, etc.
Air Nomads:
I think this one is a given. They've basically been established to be peaceful, spiritual monks since before Wan's era, and this has never changed. Only thing that has changed is the establishment of the air temples which presently have not existed for very long. 200 years max. Maybe 100. Flying bison have not yet been discovered either. Most air benders at this time are primarily nomadic, using the temples as way points, educational hubs, and for reunions. It is where young monks are born and raised until old enough to live the nomadic lifestyle (in smaller doses at younger ages and more and more as they get older), something every monk strives for. No monk remains in any temple for too long unless they are too old to travel, in which case they'd end up serving their people from the chamber of elders. Air nomads are universally adored and respected by all people of the world as they are neutral and will provide help and wisdom to anyone despite their nature. For this reason, it is a normal occurrence that, when an air nomad makes their presence known somewhere, they are always given a place to rest and food to eat.
