Short answers, pulled from the story.
The Polish-Lithuanian-Teutonic War, also called the Great Teutonic War, took place between 1409 and 1411. It began with a Teutonic invasion of Poland in August 1409 and formally concluded with the Peace of Thorn on the 1st of February 1411.
The war was triggered by a Samogitian uprising in May 1409 against Teutonic rule. Lithuania supported the uprising, Poland backed Lithuania, and Teutonic Grand Master Ulrich von Jungingen responded by declaring war on both kingdoms on the 6th of August 1409. Underlying causes included long-running disputes over Samogitia, rival territorial claims, and competition over trade routes along the Neman, Vistula, and Daugava rivers.
The Battle of Grunwald was fought on the 15th of July 1410 between the villages of Grunwald, Tannenberg, and Ludwigsdorf. Grand Master Ulrich von Jungingen was killed during the fighting, approximately 8,000 Teutonic soldiers died, and around 14,000 more were taken captive. It was one of the largest battles in medieval Europe and a decisive defeat for the Teutonic Knights.
The Polish-Lithuanian army delayed its advance after the battle, staying on the field for three days and then marching at roughly 15 km per day. The main force did not reach Marienburg until the 26th of July, by which point Heinrich von Plauen had organized the city's defenses. The besieging army also suffered from ammunition shortages, low morale, and an epidemic of dysentery, and the siege was lifted on the 19th of September 1410.
Under the Peace of Thorn, signed on the 1st of February 1411, the Teutonic Knights ceded Dobrzyń Land to Poland and agreed to give up their claims to Samogitia during the lifetimes of Jogaila and Vytautas. The Knights also had to pay a silver indemnity estimated at ten times the annual income of the King of England, payable in four installments.
The Knights never recovered their former power after the war. The financial burden of the indemnity forced them to borrow heavily, confiscate church property, and raise taxes, sparking revolts in cities including Danzig and Thorn. The loss of a religious justification for crusading made recruiting volunteers nearly impossible, and growing internal unrest led to the formation of the Prussian Confederation in 1441 and ultimately the Thirteen Years' War of 1454.