Short answers, pulled from the story.
Grand Admiral Karl Dönitz led the Flensburg Government as Reichspräsident, with Lutz Graf Schwerin von Krosigk serving as Leading Minister. Hitler had named Dönitz his successor as President and Supreme Commander in his political testament before dying by suicide on the 30th of April 1945.
The government took its name from the town of Flensburg in northern Germany, near the Denmark-Germany border, where Dönitz's command relocated on the 3rd of May 1945. The sports school at the Mürwik Naval School served as its headquarters.
The Flensburg Government was dissolved on the 23rd of May 1945, when British troops of the Cheshire Regiment and the Herefordshire Regiment carried out Operation Blackout, arresting the entire cabinet as prisoners of war. The dissolution was formalised on the 5th of June 1945 by the Berlin Declaration.
Dönitz and his cabinet hoped the Western Allies would allow them to function as a provisional German government and thus survive the end of the war. They also sought to negotiate partial surrenders to Western forces while continuing resistance against the Soviets, aiming to split the Allied coalition. Neither goal succeeded.
Herbert Backe, who remained Minister for Food and Agriculture, had authored the Hunger Plan of 1941, a deliberate strategy to starve Soviet prisoners of war and urban populations. Wilhelm Stuckart had attended the Wannsee Conference of January 1942. Albert Speer's deputy was Otto Ohlendorf, who had directed the murder of hundreds of thousands of Jews and Communists in occupied Soviet territory.
Around 10,000 concentration camp prisoners, mostly former inmates of Neuengamme, were loaded by the SS onto unseaworthy ships in the Bay of Lübeck between the 16th and the 28th of April 1945. On the 3rd of May 1945, the Royal Air Force sank the flotilla, believing the ships were being used to evacuate SS leadership. Over 7,000 prisoners drowned, the majority aboard the former liner Cap Arcona. The Flensburg Government had made no effort to free them.