Short answers, pulled from the story.
The Austro-Turkish War of 1788 to 1791, also known as the Habsburg-Ottoman War, was a conflict between the Habsburg monarchy and the Ottoman Empire fought alongside the Russo-Turkish War of 1787-1792. Austria entered the war in February 1788 as part of its alliance with Russia, and the conflict ended with the Treaty of Sistova on the 4th of August 1791 with minor territorial gains for Austria.
Austria's gains from the Treaty of Sistova were described as meagre. Despite capturing Belgrade and much of central Serbia during the war, Austria returned nearly all conquered territory and kept only the small town of Orsova and a strip of Croatian land near the Bosnian border, including Drežnik Grad, Cetin Castle, Donji Lapac, and Srb.
Disease devastated the Austrian forces. According to Braunbehrens, in 1788 the lazarettos were filled to capacity, half the army was sick, and thousands of soldiers died from epidemics including malaria. Emperor Joseph II himself fell ill at the front and died on the 20th of February 1790 after returning home.
A Serbian Free Corps of 5,000 soldiers was established in the Banat, composed of refugees who had fled earlier conflicts in the Ottoman Empire. The Corps fought for the liberation of Serbia and its unification under Habsburg rule, but their hopes were dashed when Austria returned the conquered Serbian territory under the Treaty of Sistova.
The war severely damaged Austria's economy and domestic stability. The national debt rose to 22 million gulden the year after war broke out and reached 400 million by 1790. Food prices and taxes rose, bread riots broke out after the bad harvest of 1788-89, and many aristocratic families left Vienna due to fears of conscription. Historians note that widespread disillusionment with Emperor Joseph II followed.
According to historian Rajić, the Serbs had long believed Austria would help liberate them from Ottoman rule, but the Treaty of Sistova shattered that faith. Despite Serbian sacrifices and heavy casualties fighting alongside Habsburg forces, Emperor Leopold II made peace with the Ottomans and returned Serbia to Ottoman control. From that point, Russia replaced Austria as the power Serbs looked to for support in restoring their state.