Short answers, pulled from the story.
Emperor Frederick III officially acknowledged the archducal title on Epiphany 1453 while acting as regent for his minor cousin Ladislaus the Posthumous. The elevation was conferred to all Habsburg emperors and rulers, though it did not initially carry voting rights in Imperial elections.
The region became an Imperial estate known as the Margraviate of Austria after Emperor Frederick Barbarossa issued the Privilegium Minus in 1156. This document detached the territory from the Duchy of Bavaria and established Babenberg dukes with expanded influence including the neighboring Duchy of Styria in 1192.
The territory sat within the Danube basin and ancient Roman province Pannonia Superior bordering Hungary beyond the March and Leitha rivers in the east. It extended south to the historic Semmering Pass against the Duchy of Styria and north to the Bohemian Forest and Thaya river separating Austria from Bohemia and Moravia.
The history of the Archduchy ended with the collapse of Austria-Hungary in 1918. The formal dissolution created separate federal states known as Lower and Upper Austria within the new Republic of German-Austria.
The state had been ruled by the House of Habsburg Dynasty from Frederick III until its final days. Rulers governed various states including Hungary, Bohemia, Moravia, and many others throughout the Renaissance and early modern era while serving as the nucleus of the monarchy.