Short answers, pulled from the story.
The Battle of Königsberg ended on the 9th of April 1945 when emissaries arrived at Soviet lines after Otto Lasch decided to negotiate surrender. A delegation went to Lasch's bunker and shortly before midnight the surrender was acknowledged.
Marshal Konstantin Rokossovsky directed the East Prussian offensive that included the 3rd Belorussian Front. Joseph Stalin ordered this operation to annihilate Wehrmacht forces trapped in the region.
Approximately 200,000 civilians were trapped in the city by late January 1945 when the 3rd Belorussian Front surrounded Königsberg on the landward side. Rations were cut during the siege to 180 grams of bread a day for those who stayed.
The assault started on the 6th of April 1945 after four days of preparatory artillery bombardment. Troops attacked from many points around the perimeter in a star-like plan to meet in the center of the city.
The Samland peninsula provided the only remaining escape route through that quarter until it was closed on the 29th of January. German troops held a narrow land connection to the adjacent pocket on the Samland peninsula until Soviet forces severed it.