Khazars did not convert because of outreach from Jews.
Their nobility chose Judaism because they liked it and it was a buffer to them (in modern day SW USSR region)between Cross and Crescent politically since they assumed Judaism not long after Mohammed
I woulda never guessed that 10% Jewish Roman thing.
no doubt many Jews are Semetic.....they show it physically as much as I show the cold Steppes
With 10% of the Roman Empire being Jewish (perhaps 25% in the east), with Roman Legions moving from one end of the Empire to the next, with Jews intimately involved in the Empire (at war with it, granted privileges by it and doing business with it all depending on the time frame), many if not the majority of people of European descent probably have Jewish ancestors.