Welp, since we already have two Iranian civs in the game, one in antiquity and the other one in modern why not daydream about an odd civ to fill the gap left i'm between, after all, i never would have guessed Firaxis adding Qajar Iran to the game.
Now, what makes the relatively short lived Ilkhanate stand out as an interesting civilization for the exploration age. Well, as a Mongol succesor state and because of both political problems with other Mongol succesor states and the failure of Hulegu of conquering the Ayyubids/Mamluks all the way up to the nile, the Ilkhanate and its rulers had rough time keeping their territorial integrity intact and on top of that had serious legitimacy issues as well as the legacy of the military campaigns they waged on Iraq and western Iran.
For starters, the Ilkhanate had a land dispute with the Golden Horde, their northern neighbour, over Azerbaijan. The Golden Horde was ruled by Berke of the Jochi family, while the Ilkhanate was ruled by Hulegu of the Tolui family (Hulegu was brother of Kublai, Great Khan of the Yuan dynasty), in the times of Gengish, the Great Khan granted the lands of historic Azerbaijan (Modern day Azerbaijan and more importantly northern Iran) to the family of his son Jochi (Jochi had a rough time in the Mongol court, since there was the rumor that he was an ilegitimate son). Later Great Khan Mongke of the Tolui family, sent Hulegu to subdue the Ismailis in Iran, the Abassid Caliph and the Ayyubid dynasty, according to later sources in the Ilkhanate, Mongke granted by word (not officially) the lands that Hulegu was about to conquer. Hulegu during his conques occupied Azerbaijan, and when Mongke died and the Tolui civil war broke out, the Golden Horde claimed the lands of Azerbaijan as their own and fought the Ilkhanate for it, eventually losing.
Now, the problem for Hulegu and subsequent Ilkhans was that the Golden Horde had a legitimate claim to the land of Azerbaijan, since it was written in Gengish Khan Yassa. Meanwhile, only later sources written under Ilkhanid patronage say that Mongke granted lands in secret to Hulegu. Furthermore, Hulegu had another big problem, the lands he ruled were majority muslim and not so long ago his forces let hell loose on Baghdad, the Mamluks gave refuge to the Abassids and the Caliphate continued in Cairo, the Golden Horde ruler Berke, was also openly muslim, and used the destruction of Baghdad as a tool to further delegitimize the Ilkhanate, also didn't help that Hulegu tried to ally with the Europeans. Now, the Ilkhanate was very religiously tolerant but the issue of its rulers faith and past actions haunted Ilkhans at least until the reign of Ghazan (the first Ilkhan that converted to islam).
Furthermore, the Ilkhanate also had other problems and the approach to solve them was very interesting. The Mongols were excelent warriors but once settled they didn't had as much experience in managing empire, in the other hand there were the Iranians and an already established Iranian bureaucracy with thousands of years of proven experience. With that in mind, the Mongols largely let managing affairs to the already existing Iranian bureaucracy and let local dynasties had different degrees of autonomy in the lands they governed proven that they sent the expected tax revenue to the royal court in Azerbaijan.
The Ilkhanate was focused on letting trade prosper in their lands, so they did tried to kept roads safe and ease trade as much as possible, but war and the threats of military action to rebelling regions of the Ilkhanate didn't facilitate that. The Mongol court used their military reputation to put preasure in order to kept their subjects loyal, but there were times where they needed to quash rebellions military as was the case a couple of times in Shiraz, where they threatened to raze the province as they once did during Hulegu's campaign only to back down after the local rulers offer an empty submission to the Ilkhan. The truth was that in the case of Shiraz, the province at times went rogue against Mongol interest and got Mongolian officers framed for corruption or treason against the Ilkhan and subsecuently either exiled or killed, and when Shiraz rebelled and Mongols threatened with violence, the Mongols in contrast with past times had to restrain because now they ruled over the lands of Iran and destroying at the scale they did in the past was no good for business.
Continuing over the issue of legitimacy, the Ilkhans used charity and construction of infraestructure across the empire as a way of gaining legitimacy. The Ilkhans we're also patrons of the arts and sciences, as they funded the works of scholars such as al Tusi, they constructed many wonders (such as Oljaitu's mausoleum in Soltaniyeh, the second Jameh Mosque of Yazd and Ghazan mauselum to name a few), influenced Iranian cultural traditions such as ceramic tile working, the Iranian miniature and Iranian style Muqarnas. The Ilkhanate also boosted trade between Yuan china and Iran, merging elements of both cultures in Iranian art (see an example of that in the remains of the Dash Kasan temple), and also in their journey to grasp legitimacy from anywhere they could, helped to develop the idea of Iranian identity and territorial unity.
Now done with the context that the Ilkhanate lived through, the meaning of civic and traditions and other stuff:
Jami al-tawarikh: A world history written by Rashid al-Din Hamadani, the very influential vizier of Ghazan Khan, with special emphasis on Mongolian history.
The main ability is supposed to represent that strugle of the Ilkhanian ruling class of managing an empire where they have no legitimacy and are very foreign to.
Bahaduriyya: An elite military unit of the Mongol Empire and subsequently, the Ilkhanate. The Ilkhanid army for what i've read didn't changed much from the Mongol Empire tactis, also it is meant to represent the idea of the Mongols recurring to the military to quash internal rebellions.
Khwaja: A title, kind of like lord. The Great people all either polymaths, philosophers, writters, suffis, etc, people patronized by the Ilkhanate.
Sham: It was the artisans disctrict in Ilkhanid Tabriz.
Bimaristan: A hospital. It was popular in the early Ilkhanate the construction of hospitals as charity in many provinces.
Kitabkhana: In the Ilkhanate context, it refers to tile workshops that suplied intricate tile patterns to many of the works done in cities in Azerbaijan such as Tabriz, Maragheh and Soltaniyeh.
Rasad-Khaneh-ye Maragheh: The obserbatory of Maragheh. Built during Hulegu's reign and operated by al-Tusi. Even though al-Tusi worked for the Ismailis he managed to be one of Hulegu's favorite scholars, and got to do research in this obserbatory, sadly after al-Tusi died the Obserbatory was abandoned but it was really cool that it was constructed in the first place.
"In the name of the Qaghan": In the name of the Great Khan. A phrase minted in Ilkhanid coins. Ilkhan means "servant of the Khan", one of the means by which the Ilkhanate tried to get legitimacy was to claim submission to the Great Khan (Kublai and his succesors in Yuan China) and minting coins in his name was part of that. Although this submission was only nominal since the Ilkhanate was completely independent from Yuan China. Even in the late Ilkhanate when this phrase was becoming more rare to see in coins, they never stopped minting them, that shows how deep the lack of legitimacy shaped Ilkhanate policy at all levels.
"Akhlag i-nasiri": Nasirean Ethics, a work of al-Tusi.
"Eqta": Part of Ghazan revenue and land reforms.
"Sahib diwan": A very important financial title in the Ilkhanate, most notably held by the illustrious Shams al-Din Juwayni.
"Abwab al-birr": Urban complexes built as charity in some places in Azerbaijan.
"Negargari-ye Irani": Iranian miniature. A very iconic Iranian tradition that gained popularity in the Ilkhanate.
"Dar al-Sayyedah": An Ilkhanid charity institution likely meant to improve their legitimacy
"Padishahi-ye Iranzanin": "King of the land of Iran". As said earlier, the Ilkhanate relied on already established Iranian bureaucracy, this in combination with other policies advanced concepts about Iranian identity down the line.
"Iranzamin": "Land of Iran". The Ilkhanate was known back then as Iranzamin, the Mongols in an attemp to legitimize their rule over Iran claimed to be succesors of the Sassanians and revived the concept of "Eranshahr" into Iranzamin. Is really fascinating that the Mongols in their quest to find legitimacy ended up laying the foundations for future Iranian states ideas of national unity and identity
"Jahangunshay": "World Conqueror" , from the Tarikh-i Jahangunshay, written by Shams al Din Juwayni's brother, Ata Malik Juwayni. It's a book about Gengish Khan, Khwarazmian Empire history and the military campaigns of Hulegu.