Short answers, pulled from the story.
The Soviet offensive against Vienna began on the 2nd of April 1945 when German radio denied that the capital had been declared an open city. The main assault forces advanced into the city from multiple directions starting around this date.
General Rudolf von Bünau commanded the defensive region of Vienna while SS General Wilhelm Bittrich led the II SS Panzer Corps units. Both commanders left the city before it fell to avoid capture by the Soviets and surrendered to American or Allied forces later.
Soviet Marshal Fyodor Tolbukhin's 3rd Ukrainian Front and the 2nd Ukrainian Front participated in the invasion of Austria. Romanian troops also took part in the offensive after King Michael's Coup aligned them with the Allies.
After the capture of Vienna, the city suffered from a lack of water, electricity, and gas while bands of people plundered residents without police protection. Austrian politician Karl Renner set up a Provisional Government in Vienna with tacit approval from the victorious Soviet forces.
The main fighting concluded around the 15th of April 1945 when remnants of the 6th SS Panzer Army fled toward Linz. General von Bünau was held as a prisoner until April 1947 and Wilhelm Bittrich remained a prisoner until 1954.