Short answers, pulled from the story.
The Suebi crossed the Rhine in 406 to establish kingdoms elsewhere. Some established the Kingdom of the Suebi in Galicia while others settled parts of Pannonia after the Huns were defeated in 454 at the Battle of Nedao.
Swabia emerged as one of the original stem duchies of East Francia during the 9th and 10th centuries. It was mostly ruled by two dynasties: the Hunfriding counts in Raetia Curiensis and the Ahalolfings who controlled Baar estates around the upper Neckar and Danube rivers.
The Swabian League of Cities first formed on the 20th of November 1331 when twenty-two imperial cities banded together for support. Founding members included Augsburg, Heilbronn, Reutlingen, and Ulm.
SIL Ethnologue estimated 819,000 Swabian speakers existed as of 2006 out of a total population of 7.5 million in specific regions. This figure represents roughly 10% of the total population of the Swabian region or about 1% of Germany's entire population.
In the Middle Ages, Swabia indicated a larger area covering lands associated with the Frankish stem duchy of Alamannia. This historical territory stretched from the Vosges Mountains in the west to the broad Lech river in the east and included Alsace, the later Margraviate of Baden on both sides of the Upper Rhine Valley, modern German-speaking Switzerland, Vorarlberg in Austria, and Liechtenstein.