Short answers, pulled from the story.
West Galicia, also called New Galicia, was an administrative region of the Habsburg monarchy created from territory acquired in the Third Partition of Poland in 1795. It was constituted from lands north of the Kingdom of Galicia and Lodomeria, stretching along the upper Vistula river toward Warsaw.
Austria lost West Galicia following its defeat in the War of the Fifth Coalition in 1809. After Archduke Ferdinand Karl Joseph launched an invasion of the Duchy of Warsaw on the 15th of April 1809, Austrian forces were decisively defeated at the Battle of Wagram on the 6th of July. The Treaty of Schönbrunn then transferred West Galicia to the Duchy of Warsaw.
From 1797, the seat of the local government, known as the Gubernium, was located at Kraków. The province was divided into twelve districts, with Kraków serving as both a district seat and the regional capital.
A civil code was introduced in West Galicia before the broader Austrian Civil Code was enacted in 1811. It was based on the laws of nature but contained little that addressed feudal-class problems, leaving the social structure of the territory largely unchanged.
With the Final Act of the Vienna Congress in 1815, West Galicia became part of Congress Poland, ruled in personal union by Emperor Alexander I of Russia. Kraków nominally retained its independence as the Free City of Kraków.
After the failed Kościuszko Uprising of 1794, Emperor Francis II of Habsburg and Empress Catherine II of Russia agreed to divide and completely abolish the remaining Polish-Lithuanian Commonwealth. Prussia joined that agreement on the 24th of October 1795, and the Habsburgs received the northern territory that became West Galicia as their share.