[RPG] What kinds of playing cards are used in the Forgotten Realms

At the time of my writing this answer the latest official update of Faerun seems to be dated DR1489, the last definite point in the timeline presented in Sword Coast Adventurer's Guide (SCAG). The book summarizes quite a number of world-shaking events (well, depending on what the latest you had on the world was), and if you wish to run an FR story that stays relatively close to canon (even though said canon is rather ambiguous, on purpose), it's definitely worth getting and reading through.

As for seasons and adventures, the latest we know about (again, at the time I'm writing this) is Storm King's Thunder, which has not actually been released yet, and we don't seem to have a specific in-game date for its events (yet?). Nonetheless, besides reading the official promotional material, you can also get a feel of the events it will detail (and throw at your players) by checking out Force Grey: Giant Hunters, an official(ly sponsored) actual play video series on youtube run by Matthew Mercer who uses SKT.

For previous stories, please see JAMMalcolmson's answer. :)

Given that this is a lore question, and not a specifically 5e one, I would strongly recommend the 2e product Forgotten Realms Adventures, as it has a section on 24 cities of the Heartlands with exactly the kind of information you are asking for. The catch with it is that a lot of the listed characters there are now dead (if you are playing past the Second Sundering). But even then, in terms of the social structures, most of the data are still remarkably intact. For each city in the FRA, the following information is provided: Who rules, who really rules behind the scenes, population, major products, armed forces, notable wizards, notable churches, notable rogues' and thieves' guilds, equipment shops, adventurer's quarters (lodging), important characters, important features in town, local lore and finally a small map.

As for the 3e, FR Campaign Setting (FRCS) is excellent. At 320 pages and with a small font, it is one of the most information packed D&D books ever published. (It received the Origins Award for Best Role-Playing Game Supplement of 2001.) It provides a decent amount of information on the cities, but not in the itemized format of FRA. Instead it has data on regions/countries and cities are given as individual paragraphs. So it covers a larger geography (significantly larger than FRA, or 5e Sword Coast Adventurer's Guide), but provides somewhat less detailed data on particular cities. One excellent thing in FRCS3e is a map of trade between regions.

The 4e Forgotten Realms Campaign Guide (FRCG) is structured in the same way as FRCS. However it lacks the level of detail FRCS provides. The 4e "Points of Light" philosophy is arguably reflected onto FRCG and the particular data on the cities are very limited. Moreover, 5e D&D (and the in-game mechanics of the Second Sundering) has mostly returned the setting to pretty much how it was in 2e/3e.

Finally, the 5e sourcebook Sword Coast Adventurer's Guide (SCAG) has partially returned to the style of FRA (cities are discussed explicitly), with a mix of FRCS3e. It covers more limited geography than FRCS3e, and the data on the cities is less organized than FRA (and some data are missing). Its main pro is that it happens to be the most recent published material. If one did not care about editions, FRCS3e and FRA are more suited to answer the question you have asked.

PS: Both FRA and FRCS3e are available as watermarked pdf downloads that you can buy on the web for less than half the price of SCAG.