I'll take a swing at this, but of course I am sure on this subreddit there are any number of people whose answers will be fantastic. I look forward to reading them too.

Let me start by saying when we talk about the Zulu Kingdom and the dynasty of independent Zulu kings, we are really only talking about four kings —three of whom were half-brothers— between 1818 and 1879. The political entity of kwaZulu was not an ancient institution, and a lot of the rules of the monarchy evolved between each ruler.

We should begin with Shaka. His father, Senzangakhona, was a chief of the Zulu clan. He married at least sixteen wives and had at least fourteen sons, but Shaka was not conceived in wedlock. Shaka's childhood was an unhappy one. He was rejected by most of his father's people, and grew up with his mother until he was old enough to begin his life as a warrior, where he excelled. He came to the attention of Dingiswayo, a king of the Mthethwa who combined many of the Bantu clans in the area at the time into a confederation to oppose a rival confederation of clans to the north. By the time Senzangakhona died in 1816, Shaka was a proven battlefield commander. Dingiswayo loaned him a regiment, and Shaka conquered the Zulu clan from Senzangakhona's chosen heir, incorporating the clan into Dingiswayo's power base. Two years later, Dingiswayo was captured and killed by the northern rival, and Shaka gathered up the remnants of the old Mthethwa alliance and reforged them as a Kingdom under his rule where all males were formed into regiments by age group and owed him service —active military service for unmarried warriors, and then other services once the king permitted a regiment of a given age to marry and become heads of their own household.

This organization of fighting strength combined with new unit tactics and an emphasis on close-quarter combat over more traditional methods of warfare saw the Zulu become a dominant regional power. That's actually understating it. As far as Iron Age societies with cattle-based economies go, the Zulu under Shaka were basically unstoppable. This time is now referred to as Mfecane, 'The Crushing' or 'The Scattering,' for the turmoil the rising Zulu nation caused. The traditional (controversial) death toll is over a million dead, and hundreds of thousands of others migrated out of the area, including groups that had learned Shaka's new methods of warfare and would take it with them to start their own nations elsewhere based on his model.

Over the rest of Shaka's (tyrannical) rule, his power came from military success bringing in newly conquered peoples into his kingdom who would then further build up his military power. The king decided matters of war and peace. The king decided what his regiments did in war and peace. He decided when they married. The clan chiefs he incorporated into his court feared him. Executions were arbitrary. The annual festival of First Fruits saw him gather the nation's strength in people and cattle together for a series of rituals reinforcing him as the beating heart of the nation, leader of their people, commander of their army, bestower of cattle and pasture land on favourites, and the protector of the people from misfortune from the spirt world. As King, his person was itself a magical item, and things like his hair and toenail clippings were carefully protected from collection by wizards. Much of it went into the inkatha, a collection of magical charms sheathed in snake skin.

Skipping ahead in the story, Shaka was assassinated by two of his half-brothers, one of whom, Dingane (sometimes spelled Dingaan), ruled in a very Skaha-like mold, but without his brother's charisma or military gifts. Dingane also had the misfortune of ruling as European settlers were making their way towards his territory. Conflict with the Boers stopped Zulu westward advances, and a northern frontier was also forming up along the Swazi territories, who proved difficult to conquer. Dingane went through all the same 'I am your king!' rituals of Shaka, but he was not nearly as popular as his now dead brother who was already becoming a part of Zulu mythology. Meanwhile, Dingane was paranoid of a coup from his remaining half-brothers and other Great Men of the Nation (as the greatest clan chiefs were known), and he led a series of purges that only strengthened the underground movement against him.

Mpande, another half-brother, survived these purges by playing the family idiot right up until he was sure of his moment to strike. He fled from Dingane's Court, went to the Europeans for help, and returned with 400 heavily armed Boers who became the nucleus of a popular uprising against Dingane. In the end Dingane executed his own general in an attempt to stop his forces from deserting to Mpande's cause, then fled, being murdered while seeking refuge in a nearby forest.

Mpande was the last of the sons of Senzangakhona we know about, and while his throne was won with European firepower at his back, he was still viewed as his own man while he ruled. This was not so true of his sons, however. He refused to name an heir —probably fearing assassination if he did so— but his princes fought a civil war among themselves with Cethswayo coming out on top, again with the help of Europeans. Cetshwayo waited for his father to die of natural causes (in fact, there is strong evidence he didn't broadcast his father's death until he was sure he would be able to succeed peacefully), and then he invited Europeans to his court for a coronation so the Great Men of the Nation could see there were foreign backers of his rule.

Cetshwayo was in the midst of strengthening the monarchy's powers when the Anglo-Zulu War of 1879 broke out. He reformed the regimental system, and the new regiments he formed were much bigger and more powerful than the ones Mpande had gathered during his relatively peaceful reign. This suggests Cetshwayo was successful in pulling young warriors to his capital to serve him rather than staying at home and serving their local clan chiefs as warriors in private regiments, an ongoing issue he was seeking to address even as the war broke out. Cetshwayo's festivals of first fruits were strengthened by his association with the uSuthu breed of cattle, whose bull he took as a personal brand. In fact, the most popular Zulu war cry during the Anglo-Zulu was, "uSuthu!" Which is a positive affirmation of Cetshwayo's popularity among his army, something Mpande and Dingane likely could not boast, and even Shaka was more admired and feared than necessarily popular or seen as having right on his side.

For all that, the Zulu Monarchy was a shaky thing. Shaka built a military dictatorship out of fragments of his dead patron's regime. His killer tried to rule it the same way with mixed results. His killer's ouster used European firepower to win power, then lost a lot of power to regional clan chiefs and his princes during his reign. Mpande's greatest accomplishment is being the only Zulu king of the independent Zulu Kingdom to die of natural causes. Cetshwayo may have been at the cusp of a Golden Age based on a strengthened monarchy with reinvigorated military traditions, a strengthened central government, and impressive First Fruits Festivals, but he did not have time to finish it before war broke out.

Sorry, this turned into a longer answer than I meant it to be. To learn more about the Zulu in the 19th Century, my favourite single volume on Zulu history is The Rise & Fall of the Zulu Nation by John Laband, but I confess I feel a little bad flagging his one book to your attention when Ian Knight has written more than 50 books on the Zulu. You're always in pretty good hands with him too. I also enjoyed reading Shaka's Children: A History of the Zulu People by Stephen Taylor, although I remember thinking as I read it that Laband really did cover everything in his book to the point it felt there was very little new content to discuss.

Edit: Apologies. I posted this and was away for the evening. This morning I found a couple of typos. I also cleaned up one or two sentences that could use sharpening.