Harald Hardrada actually sent expeditions to try and find a northern route to Asia. Perhaps they could discover the Ob. I think OTL they made it to Novya Zemalya
Hardrada was a fascinating man, he's forever remembered as the brute that failed to take England from Harold Godwinson, but his fame as a brilliant commander serving the Byzantines was far more interesting. If his men does discover the lucrative opportunities of the Northeast passage I wonder how this might change his plans to invade England. William will probably still win, but it's not assured.
A Varangian Guard in the service of a Song emperor would be interesting.
As far as Mongols attacking, who knows. A string of fur towns in Siberia isn't exactly going to be high up on the priority list of any khan.