2.) Zhu Houzhao (Zhengde Emperor) x Yang Tinghe

朱厚照 Zhu Houzhao (1491/10/26-1521/4/20): Only son of his parents, his father famously had no harem only a single wife, so somewhat of a spoiled and naughty child. Not very healthy but rebellious and much more interested in military conquest and living up to his ancestors' glory than civil affairs, constantly sneaking out of Beijing to go hang out in Datong and other border towns. He also gave himself an alias of a great general and duke named Zhu Shou. Somehow he never feels out of character unless he is actually acting like a good emperor. Certainly gets into fights with Yang Tinghe but trusts him the most, and they both know it (and this is backed up by historical writings from Yang Tinghe and records of things Zhu Houzhao said).

Leopard because he built a "leopard house" where he kept various animals and people and liked to hang out there instead of the palace.

杨廷和 Yang Tinghe (1459/10/15-1529/7/15): Young genius to teacher of the most important and also extremely rebellious student. Eventually became the most important person in the Zhengde government beneath the emperor. The two of them butt heads but Yang Tinghe is never punished for going against the emperor's wishes, they just have some "silent treatment" ignoring each other periods. Characterized as extremely strongly believing in traditional Confucian values and thus very anti most of Zhu Houzhao's behavior (for instance his alias, because the emperor shouldn't be giving himself a lower rank), but also has an 800m thick rose-tinted glasses view of Zhu Houzhao (he's a good kid he just keeps falling in with bad company...). Also extreme workaholic because Zhu Houzhao is always slacking off, and Zhu Houzhao's moral police always ready with a historical example and lesson.

Sheep because of his surname, or a crane sometimes.

杨慎 Yang Shen (1488/12/8-1559/8/8): The "son who's older than me", Yang Tinghe's eldest son and the one who's always having to suffer in these ship fics as the "bride's family" role ("stay away from my father!"), jokingly called "little pepper of Sichuan" because his personality is very direct and bold (see his role as the "warrior god of Zuoshun gate 2.0", 1.0 happened under Zhu Qiyu). He's also a genius who wrote the famous poem 临江仙 that was used as the theme song of the Romance of the Three Kingdoms. Sometimes Yang Tinghe's other sons are also involved but none of them are as bold and angry as Yang Shen.

Common meme in the community is Zhu Houzhao saying "we'll each consider it separately, I call you older brother and you call me dad".

王琼 Wang Qiong (1459-1532/8/22): Yang Tinghe's political enemy, although in a lot of fics he goes from fighting with Yang Tinghe for Zhu Houzhao's favor to the realization "actually I'm not jealous at all that His Majesty favors you more".

蒋冕 Jiang Mian (1463/3/1 or 11/22-1532/8/12): Yang Tinghe's ally, his "toxic solo fan". Also jokingly called Auntie Jiang because Yang Tinghe had one concubine whose surname was the same Jiang. Kind of a "bride's family" faction member like Yang Shen.

李东阳 Li Dongyang (1447-1516): Yang Tinghe's superior before he retired and Yang Tinghe took his place, extremely influential poet who developed the Chaling style, recorded in history as "humorous but not attractive in appearance" (as opposed to Yang Tinghe who was attractive... Ming emperors and their appearance bias is also a meme), usually he's the guy who's looking on from the sidelines metaphorically eating sunflower seeds and collecting gossip to write about. Fun fact is he's also a child prodigy, in fact he was so well known as a prodigy that he met Zhu Qiyu when he was four and Zhu Qiyu was very impressed by him.

Then there's Zhu Houzhao's various cabal of "bad company" aka his eunuchs and "adopted sons" (but not officially, just "for fun") that he's always running off with, many of whom Yang Tinghe had pretty brutally executed after Zhu Houzhao's death.

朱厚熜 Zhu Houcong (1507/9/16-1567/1/23): The Jiajing emperor who succeeded Zhu Houzhao when he died young with no heir. For legitimacy reasons, he should've posthumously been adopted as Zhu Houzhao's brother (he's actually his cousin) but he didn't want to do that, he wanted to instead make his own father posthumously an emperor. In order to preserve the legitimacy and continuity of Zhu Houzhao's family line Yang Tinghe fought politically with him to force him to give up on that idea, but ultimately Yang Tinghe failed and was stripped of his titles and rank and demoted to a commoner, so Zhu Houcong is definitely the villain of this ship. Also he was not a very good emperor... very intelligent but not interested in using that intellect to improve the dynasty, only interested in using it for personal gain. Also this guy was obsessed with Daoism and immortality and was probably eating heavy metals every day in pursuit of that yet he somehow lived to be 60, I can only say some people are built different... special talents indeed.

Also he's green onion, because that's what the cong in his name sounds like. When I was in a museum looking at an artifact from his reign I heard a guy confidently pronounce his name Zhu Houzong to his girlfriend and I rolled my eyes so hard.

3.) Zhu Yijun (Wanli Emperor) x Zhang Juzheng

朱翊钧 Zhu Yijun (1563/9/4-1620/8/16): Sweet child who respects his teacher Zhang Juzheng to slowly more and more resentful teenager who hates that his authority as emperor is eroded by Zhang Juzheng essentially serving as effectively the regent when he ascended the throne at age 10. Finally his dark and twisted side comes out after his teacher dies and he ruins all his reforms, starves 10+ members of his household to death, drives his eldest son to kill himself in prison, and in his search for the wealth he's sure Zhang Juzheng must be hiding somewhere, almost desecrates his grave. In reality Zhang Juzheng had very few burial goods -- only a belt and inkstone the emperor gifted him when he was younger. He's the villain of his own story, the ship is extremely cursed sort of "I hate him so much but I hate that he's dead", any happy ending usually involves Zhu Yijun having to reborn after suffering punishment in either being reborn as a peasant/animal for a few lifetimes or getting the shit kicked out of him by his ancestors after death, etc. We can directly contrast him with Zhu Houzhao in regards to how they treated their teachers. If only he never grew up and was just his teacher's young student who made him noodle soup when he was sick and promised to protect the Zhang family so that they shared the fortune of the dynasty (in some ways they did because after Wanli's death the Ming Dynasty ended within a few decades, shockingly quickly because in the early Wanli era due to Zhang Juzheng's reforms things were looking up).

He's a pig. Because the Ming royal line's surname is Zhu, also he was overweight later in life. He actually had an ancestor who was overweight too, but that ancestor Zhu Gaochi is well remembered as a merciful emperor (actually he was only emperor for a year or so but he was crown prince for a long time and had to manage affairs while his father was off on military campaigns) so only Zhu Yijun gets the "pig" emoji. (There's theories that the second emperor Zhu Di's Empress Xu had type I diabetes in her family.) He's also sometimes called "disinfectant" because yijun sounds like antimicrobial. He's a pretty hated emperor so that's why he only has negative nicknames.

张居正 Zhang Juzheng (1525/5/26-1582/7/9): One of the big three reformists of pre-modern China. Also a young genius, maybe not the most morally pure person like Yu Qian, but probably the only person who could have saved the deteriorating Ming Dynasty at that time. He could have lived an easy and comfortable life but instead he chose to risk it all to fix the problems he saw in the government, and he met a ton of resistance and pressure, as all reformists do. Most of the anti-Zhang action happened after he died, so although he certainly knew his end probably wouldn't be good, he probably didn't imagine Wanli would take it to that extreme. Usually characterized as still having a soft spot for the child that he half-raised and probably spent more time with than his own sons. Zhang Juzheng actually didn't live that long compared to his family members who managed to die natural deaths, same lifespan as Wanli, in fact, and the general interpretation is he worked himself into an early grave.

Actually his name at birth was 白圭 Baigui but was changed before he took the imperial exams because it wasn't really a scholar's name, because of this original name he's a white tortoise and there's a lot of cute fanart of this.

Because Zhang Juzheng is the "succubus/incubus" of the Ming Dynasty, there's so many other people he's shipped with. Most notably:

高拱 Gao Gong (1513/1/19-1578/8/4): Zhang Juzheng's close friend before he was ousted by him in a political struggle and their relationship deteriorated, also the teacher of Wanli's father the Longqing Emperor Zhu Houji. Famously wrote in his "Last Words on My Sickbed" that one time "the jingren came to my courtyard in his inner clothes" where jingren could mean person from Jingzhou (which Zhang Juzheng was from) or in some contexts wife. It's the most commented on line in the WeChat Books app.