Short answers, pulled from the story.
The Swiss businessman Jean-Henri Dunant founded the movement after witnessing the aftermath of the Battle of Solferino on the 24th of June 1859. He published A Memory of Solferino in 1862, calling for national relief societies and an international treaty to protect the wounded. He worked alongside Gustave Moynier, Louis Appia, Theodore Maunoir, and Guillaume-Henri Dufour in the group known as the Committee of the Five.
The First Geneva Convention was adopted on the 22nd of August 1864 in Geneva, where 16 countries sent 26 delegates. Its ten articles created the first legally binding rules guaranteeing neutrality and protection for wounded soldiers and field medical personnel in armed conflict.
The movement officially recognizes the Red Cross, Red Crescent, and Red Crystal emblems, with the Red Lion and Sun also official though fallen into disuse. The Red Cross was approved in Geneva in 1863, the Red Crescent was officially adopted in 1929, and the Red Crystal was adopted on the 8th of December 2005 under Protocol III.
The ICRC was criticized as early as May 1944 for indifference to Jewish suffering and failed to obtain an agreement with Nazi Germany over concentration camp detainees. After November 1943 it registered about 105,000 detainees and delivered about 1.1 million parcels, primarily to Dachau, Buchenwald, Ravensbruck, and Sachsenhausen. Individual delegates such as Friedrich Born in Budapest saved between 11,000 and 15,000 Jewish people in Hungary.
The ICRC received the Nobel Peace Prize in 1917 and again in 1944, each the only Peace Prize awarded during the main period of those world wars. The ICRC and the League of Red Cross Societies shared a third prize in 1963 for the movement's centennial. Founder Jean-Henri Dunant also shared the first-ever Nobel Peace Prize in 1901 with Frederic Passy.
The ICRC, headquartered in Geneva, protects victims of international and internal armed conflicts and is composed only of Swiss-citizen members. The IFRC, founded as the League of Red Cross Societies in Paris in 1919, coordinates the national societies and leads relief in emergencies not caused by war, such as natural disasters. As per the 1997 Seville Agreement, the IFRC is the Lead Agency in any non-armed-conflict emergency.