Short answers, pulled from the story.
The Polish government-in-exile was formed in the aftermath of the September 1939 invasion and occupation of Poland by Germany, the Soviet Union, and the Slovak Republic. Władysław Raczkiewicz took the presidential oath in Paris after Ignacy Mościcki resigned in late September 1939.
The Polish government-in-exile was based in France during 1939 and 1940, first in Paris and then in Angers. After the Fall of France it relocated to London, where it remained until its dissolution in 1990.
The Polish government-in-exile broke relations with the Soviet Union after Stalin severed ties in 1943, when the exile government refused to accept the Soviet denial of responsibility for the Katyn massacre. German authorities had announced the discovery of the mass graves at Katyn Wood in April 1943.
Ryszard Kaczorowski was the last president of the Polish government-in-exile. On the 22nd of December 1990, he handed the presidential insignia to Lech Wałęsa at a ceremony in the Royal Castle in Warsaw.
The Polish government-in-exile lost recognition from most states after the Provisional Government of National Unity was formed, with France withdrawing recognition on the 29th of June 1945 and the United States and United Kingdom following on the 5th of July 1945. The Holy See was the last country to withdraw recognition, on the 19th of October 1972.
Polish soldiers fought under commanders answering to the Polish government-in-exile as part of Allied forces in Europe, Africa, and the Middle East, including at the Battle of Britain, Tobruk, and Monte Cassino. Anders' Army, formed from Poles released from Soviet captivity in 1941, transferred through Iran to fight alongside British and American forces.