Short answers, pulled from the story.
The East Prussian offensive was a strategic Soviet Red Army campaign against the German Wehrmacht on the Eastern Front of World War II. It ran from the 13th of January to the 25th of April 1945, and its centerpiece, the Battle of Königsberg, ended in a Red Army victory.
The East Prussian offensive lasted from the 13th of January to the 25th of April 1945. Some German units did not surrender until the entire country did, on the 9th of May.
Ivan Chernyakhovsky's 3rd Belorussian Front carried the main thrust toward Königsberg. General Hovhannes Bagramyan's 1st Baltic Front supported the right flank and Marshal Konstantin Rokossovsky's 2nd Belorussian Front supported the left flank.
German historians use that name because an earlier attempt, the Gumbinnen Operation, ran from the 16th to the 27th of October 1944 under the 3rd Belorussian Front. That first attempt was postponed after heavy casualties, so the Red Army launched a larger second offensive in January 1945.
The siege of Königsberg trapped the remnants of the 3rd Panzer Army inside the city under 4th Army command. After massive casualties on both sides, Soviet forces took Königsberg on the 9th of April 1945.
German units kept fighting on the Vistula Spit, the long sandbar enclosing the Vistula Lagoon, until the end of the war. This continued even after Soviet forces cleared the port of Pillau on the 25th of April, in the Samland offensive.