Short answers, pulled from the story.
The Continuation War began on the 25th of June 1941 with a Finnish declaration of war on the Soviet Union and ended on the 19th of September 1944 with the signing of the Moscow Armistice. The conflict lasted just over three years.
Finland's primary motivation was to reclaim territory lost under the 1940 Moscow Peace Treaty, which had stripped the country of 9% of its national territory after the Winter War. Some Finnish leaders, including President Risto Ryti, also envisioned a Greater Finland incorporating East Karelia and other Finnic territories. Finland cooperated with Germany while officially describing itself as a co-belligerent rather than an ally.
Finnish forces cut the city's northern supply routes and halted their advance roughly 30 km from the center of Leningrad, but the full extent of their participation is disputed among historians. Mannerheim personally refused Hitler's request to assault Leningrad during their meeting on the 4th of June 1942. Historians disagree on whether Finnish actions constituted active participation in the siege or a more limited contribution.
Finland was required to return to the borders of the 1940 Moscow Peace Treaty, pay war reparations initially set at $600 million and later reduced to $300 million, cede the municipality of Petsamo, and lease the Porkkala Peninsula to the Soviet Union. Finland was also required to expel German troops from its territory by the 15th of September 1944, which led to the subsequent Lapland War between Finland and Germany.
Finland's approximately 2,000 Jewish citizens served in the Finnish Army alongside other Finns, with a functioning synagogue operating in East Karelia. When SS leader Heinrich Himmler raised the question of Finnish Jews in the summer of 1942, Prime Minister Jukka Rangell stated that Finland had no Jewish question. In November 1942, Interior Minister Toivo Horelli and State Police chief Arno Anthoni secretly deported eight Jewish refugees to the Gestapo; only one survived. After that incident, the Finnish government refused all further transfers to German custody.
The Battle of Tali-Ihantala took place from late June through the 9th of July 1944 and has been described as the largest battle in Nordic military history. It was the decisive engagement during the Soviet Vyborg-Petrozavodsk offensive, in which Finland, with German anti-tank weapons and reinforcements including the 122nd Infantry Division, halted the Soviet advance after retreating roughly 100 km. The Finnish Army held the Viipuri-Kuparsaari-Taipale defence line and stabilized the front.