I've recently been watching Micheal Hirst's 'Vikings' (which is fantastic), and it has thrown up a few questions about its rough time period (the 9th century, I believe).
One of which is on the subject of slave trading at the time. In the late stages of the current stages (potential spoiler alert for those who want to watch the show), the protagonist befriends a slave of Chinese-origin, who had, through a long series of exchanges (the last being the Franks), wound up in Scandinavia.
Was this common place? Did slaves from considerably distant continents and kingdoms manage to travel that far through war and exchanges? If so, how much do we know about their lives in a completely alien environment? (I predict not much, considering they were slaves)
The precursor to the silk road of Genghis Khan times was the Persian Royal road built about 500BCE. This went from northern Iraq to Turkey and was extended during Alexander the Great's reign. About 200BCE China was referred to as "the place where silk comes from" and eventually the roads going from coast to coast were called the Silk Road which was actually many roads not just a single one.
So to answer the questions in two parts:
There have basically always been slaves.
Even as far back as 500BCE during the Persian Royal Road there were horses and postal stops. You could trade out tired horses for fresh horses and mail could go from Iraq to Turkey. This was greatly extended through generations. This road is also, many theorize, how the Bubonic Plague jumped from Asia to Europe much later on. So yes, absolutely, having a person of Chinese decent during 900-1000 would be quite possible.
Add to this that Russia, The Rus, were termed by the vikings and that's where the name comes from. The vikings were quite pervasive back then and gaining the ownership of foreign slaves would be typical.
It's possible but not probable. Trade routes did stretch from Scandinavia all the way to China, largely through Islamic middlemen. Unfortunately for Michael Hirst, the Islamic world was importing slaves, not transshipping them, so the chances that a Chinese slave would have made it all the way up into the world of Ragnar Lothbrok (if there was a Ragnar Lothbrok) are pretty slim.
I wrote more at length about this here and later here, which started some interesting discussions. But since comments are closed on both threads, feel free to ping me for further here. There was also another conversation at about the same time about how far Norse travelers may have gone, which might also be of interest.