(1) There was always a large amount of movement between the Sephardic and Ashkenazic communities. The Rosh (Rabbi Asher ben Yechiel), born in Germany, became the chief Rabbi of Spain in the 13th century, for instance. A significant number of Sephardic refugees fled to Holland in 1492, whence they moves to Germany and Poland (my wife’s family among them). This is how such names as Gratzia (Gracia), Shprintza (Esperanza), and Vita became Yiddish girls’ names.
(2) The “Iraqi” Jews in the article must be the so-called “Kurdish” Jews of northern Iraq, who represented the original Jewish exile population who remained. The Baghdadi Jews were “imports”, as it were, from Syria and elsewhere when Haroun el-Rashid built Baghdad on the site of the small town of Bagdëtha’a (mentioned in the Talmud) and made it his capital.
(3) The story of Khazaria is usually misunderstood and misrepresented. The Khazars were a Turkish tribe who converted to Judaism about 1,300 years ago (cf. Rabbi Yehuda ha-Levi’s “Kuzari”). Thereafter, as numerous references in both Chritian and Muslim sources show, Jews flocked to Khazaria from both the Eastern Roman Empire and the Muslim lands when those regimes became too onerous. As well, Rabbi Pëthachya of Ratisbon, in his Sivuv ‘Olam, records that he met Khazars when he visited Bavel; they were recruiting rabbis and teachers for their communities from the great Babylonian yëshivoth.
The Khazar state was destroyed in the 10th century by Sviatoslav of Kiev, and its population – ethnic Jews and ethnic Khazars alike – were scattered across eastern Europe, where they were absorbed into the Yiddish-speaking immigrants from Germany, when Boleslaw Chrobry invited German Jews to settle in Poland, in the 14th century.
Especially strong was the Khazar element in Hungary. One of the tribes who made up the Magyar coalition which burst into the Puszta in the 10th century consisted of Khazars, who settled primarily in the Erdély (Transylvania). There are Jewish tombstones in the region from this period, and Transylvania also was the location of the largest number of converts to Judaism from amongst the Hungarian-speaking population, which was constantly being accused of “Judaizing” tendencies by the Catholic church.