Short answers, pulled from the story.
An estimated 100,000 men were arrested as homosexuals between 1933 and 1945. Around 50,000 were sentenced by civilian courts, between 5,000 and 6,000 were imprisoned in concentration camps, and the death rate among concentration camp prisoners has been estimated at 60 percent.
Paragraph 175 was a provision of the German penal code, originally passed in 1871, that criminalized sexual acts between males. A 1935 revision dramatically broadened the law to punish virtually any homosexual act, including embracing or mutual masturbation, and applied the new standard retroactively, leading to a sharp rise in arrests and convictions.
The pink triangle was a badge imposed on homosexual prisoners in Nazi concentration camps, standardized in 1938. After the war, LGBT activists reappropriated the symbol as an emblem of gay liberation, using it to connect the history of Nazi persecution to ongoing discrimination against LGBT people.
West German president Richard von Weizsäcker gave the first official recognition of the Nazi persecution of homosexuals in 1985. Germany annulled Nazi-era convictions under Paragraph 175 in 2002 and offered compensation to survivors in 2017, including those convicted after 1945 under laws inherited from the Nazi state.
Homosexual survivors were not recognized as victims of Nazism because homosexuality remained illegal in West Germany. Those who had not finished serving their sentences under Paragraph 175 had to continue doing so, and between 1945 and 1969, West Germany convicted approximately 50,000 men for consensual homosexual acts, the same number convicted during the entire Nazi period.
The killing of Ernst Röhm on the 30th of June 1934 marked a turning point. Nazi propaganda cited Röhm's homosexuality to justify the purge, and in its aftermath Heinrich Himmler consolidated control over the SS, the Gestapo, and the concentration camp system. A dedicated Gestapo department targeting homosexuals was established within months, and by early 1935-80 percent of those held in protective custody in concentration camps were there for alleged homosexuality.