Short answers, pulled from the story.
Olaf Tryggvason was born in the 960s, with specific dates ranging from 963 to 969 according to various sagas. He spent his early years fleeing to Kievan Rus after his mother Astrid Eiriksdottir escaped killers of his father.
Queen Geira, a daughter of King Burizleif, married Olaf Tryggvason after they met in 982. She died three years later around 984, prompting him to leave Wendland and begin plundering again.
Jarls Haakon became unpopular due to taking elite daughters as concubines and fighting Danish kings while rejecting Christianity. Olaf seized this opportunity to sail for Norway where rebels accepted him as king after Jarl Haakon was killed by his slave Kark.
Olaf Tryggvason founded his seat of government in Trondheim in the year 997. The location was chosen because the River Nid created a defensible peninsula that could be protected with only one short wall.
Olaf Tryggvason died at the sea Battle of Svolder when his forces were defeated by a combined armada from Denmark, Sweden and the Jarls of Lade. Danish sources report he committed suicide by throwing himself into the sea while wearing full armour.