Short answers, pulled from the story.
The Austrian Empire declared war on Napoleon on the 8th of February 1809 because Foreign Minister Johann Philipp Stadion and diplomat Klemens von Metternich cited the 1808 French disaster at the Battle of Bailén as justification. Archduke Charles had spent three years improving the army after the War of the Third Coalition but faced deficiencies in staffwork and non-German nationalities.
The Battle of Teugen-Hausen occurred on the 19th of April 1809 when Saint-Hilaire's advance elements blundered into the III Armeekorps marching column at Hausen. The fighting ended at 5:00 pm that day after a violent thunderstorm swept across the area.
Austrian casualties ranged from 3,463 to 3,862 depending on the historian, with figures including 527 killed, 2,470 wounded, and 466 captured according to official admissions. Austrian general officers suffered unusually heavy losses, including brothers Alois and Moritz Liechtenstein who were both wounded.
The battle took place on a wooded height approximately halfway between the villages of Teugn and Hausen in Lower Bavaria. This location lies two kilometers southwest of Herrnwahlthann or Thann.
Marshal Louis-Alexandre Berthier organized the Armée d'Allemagne but Napoleon took over command early on April 16. Marshal Davout led the French troops that engaged Archduke Charles's III Armeekorps under Feldmarschall-Leutnant Prince Friedrich Franz Xaver of Hohenzollern-Hechingen.