So this is a multiple part question, looking through the wikipedia article of the Mongol Empire the oldest written piece of literature ("The Secret History of the Mongol") was written after Genghis Khan's deaths I was wondering if this is what most histories are based on (apart from other nations accounts)? And if this is the case is the phrase "history is written by the victor" actually correct? Could the events that we know about be skewed by the fact that mostly the "losers" were writing the history?
"History is written by the victors" is not always true. Indeed, history is always written by the literate and this may be the conquered or conquered, or both. Think of the Huns: they conquered swathes of land in Europe and were one of the causes of the Western Empire's fall. Yet we know precious little of their ways due to most information we have of them coming from Roman sources, who sometimes just depict them as half men half horse monsters. Same with the Mongols, we have Chinese written records and some European, though few beyond that.