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. :)
The overall demographics of modern Forgotten Realms, ie. say the last couple centuries, seem not to have changed much over the various editions of the game. Since around -3000DR, when the human archmage Iolaum raised the first enclave of what would become the Netherese Empire, humans have been increasing in influence, while the dwarven and elven empires have declined ("Age of Humanity").
For individual cities, detailed statistics are available in Forgotten Realms Adventures (2e) and Forgotten Realms Campaign Setting (3e FRCS). Certain locations, like Evermeet or Luiren, are exclusively or mostly non-human (elves and halflings respectively); others are mentioned to have significant non-human populations like Lantan (gnomes). However most of the settlements on the surface of the continent of Faerun are predominantly human. You can get some of these data (even exact percentages) on the FR wiki.
If you are interested not in particular locations, but in the overall percentage, we can say that humans are the dominant species. In order to get data about the whole planet altogether, it would be meaningful to refer to a sourcebook that considers the whole planet as a unit, as it is observed literally from space: In the 2e game accessory Realmspace, the population analysis is summarized (page 18) as follows: "Human and humanoid races most prevalent".
Finally on the RPGnet forums, a poster with the nickname Handigar claims to have added up all the data from FRCS. Quoting from that post:
- Faerun's total sentient population is about 66 million, roughly comparable to modern Britain or the Roman Empire.
- Humans are the most common race, at over 80%.
- After humans, halflings are most common with 3.5 million, followed closely by Dwarves. Elves and Orcs are rare outside their concentrations.
Best Answer
Yes, for at least a century or more
Printing presses are known to exist in the Realms for more than a century. There is a short story by David Cook named Patronage in the 1993 anthology Realms of Valor. The story takes place in Procampur in 1362DR and describes the surprise of a Tuigan lama, Koja, upon seeing a printing press for the first time and his attempt to get his A History of the Tuigan to be mass-published.
There is also a 4-part series of articles by Ed Greenwood, titled Small Presses of Waterdeep, published on the WotC website in 2003 (again the similar time period DR). These are still available on the web, where you can read about the printing presses and bookshops of Waterdeep.
While the Spellplague seems to have caused some harm, the printing business seems to have recovered quickly and the situation in 1490s is not much different in much of Faerun according to unofficial tweets by Ed Greenwood: