Short answers, pulled from the story.
The Finnish War began because Russian Emperor Alexander I demanded that Sweden cut off trade with Britain under the Treaty of Tilsit. King Gustav IV Adolf refused to comply, leading to military conflict starting in 1808.
Hostilities started on the 21st of February 1808 when Russian troops crossed the border at Ahvenkoski. The war concluded with the signing of the Treaty of Fredrikshamn on the 17th of September 1809.
Sweden lost control of Finland after being defeated by Russian forces throughout 1808 and early 1809. The Treaty of Fredrikshamn signed on the 17th of September 1809 officially ceded all of Finland plus domains east of Torne river to Russia.
About 21,000 Swedish troops were stationed in various fortresses across Finland while the rest of the army remained unable to leave southern Sweden due to fear of Danish attacks.
The fortress of Sveaborg surrendered on the 6th of May 1808 after negotiations concluded resistance was futile despite having a garrison of 6,000 men and over 700 cannons. Russians gained the main body of the Swedish archipelago fleet intact along with large supplies from this capture.