Short answers, pulled from the story.
Jean-Baptiste Jules Bernadotte was born on the 26th of January 1763 in Pau, the capital of Béarn. He entered the army as a private soldier on the 3rd of September 1780 within the Régiment Royal, La Marine.
Baron Carl Otto Mörner offered the Swedish crown to Bernadotte entirely on his own initiative in 1810. The Riksdag of the Estates elected him heir-presumptive on the 21st of August 1810 after considering various candidates including Eugène de Beauharnais.
Bernadotte commanded the Army of the North during the Battle of Leipzig which began on the 17th of October 1813. His fresh troops joined the fray against already battered French lines on the 19th of October and committed the final blow to the depleted French forces.
A brief campaign saw the defeat of the Danish Army and forced King Frederick VI to sign the Treaty of Kiel on the 15th of January 1814. This treaty ceded Norway to Sweden as stipulated in several treaties creating the Sixth Coalition.
The military operations became Sweden's last direct conflict to this day. Charles John accepted the Constitution of Norway instead of naming harsh terms, which paved the way for Norway to enter a personal union with Sweden later that year.