There have been several questions (with answers) on the Mongol Invasions of Japan in the past, for example here , here , here , and here.

Furthermore, related to the game's historical accuracy, you can also find this and this thread.

(note: answers in these linked threads have been given by u/ParallelPain , u/krishaperkins , u/wotan_weevil , and u/Erina_sama )

To summarize, yes Yuan China, which was under Mongol rule at the time, indeed launched two large-scale naval invasions in 1274 and 1281, and retreated both times. In both cases, typhoons were given as the reason for their "defeat" (although that is debatable). The island of Tsushima, which is closer to the Korean peninsula than to Japan proper, was attacked first and overrun (there were only about 80 warriors on the island, who all were slaughtered pretty much instantly).

Although the team did travel to Tsushima and took inspiration from the real-world island for their location design (for example, the castle actually existed), the characters and the plot are entirely fictional. The clothing, weapons and armor are mostly ahistorical, stemming from later historical periods.

The whole "bushido" and "samurai" blabla is pretty nonsensical, since neither did warriors at the time self-identify as "samurai" - which is a development of the later Edo-period, when the warrior elite became socially locked into being a samurai "caste" - nor did the whole code-of-honor-"bushido" exist in this form, since that is a fictional creation loosely based on, mostly, Edo-period writings, constructed in the late 19th/early 20th century.

For more information regarding these and other things, check the other questions and their respective answers :)