Short answers, pulled from the story.
The two main types of punishment under medieval Scandinavian law were fines and outlawry. Fines, called mulcts, were by far the more common outcome and varied based on the severity of the offense and the social status of both the accused and the victim.
The Gray Goose Laws, known in Icelandic as Grágás, were a written collection of laws from the Icelandic Commonwealth period. The Althing decided in 1117 to write all laws down; the work was completed at Hafliði Másson's farm that winter and published the following year.
A holmgang was a formal duel between the accuser and the accused, used in early medieval Norway to determine the outcome of a legal dispute. The winner was considered to have the favor of the gods and was treated as the innocent party.
Magnus Lagabøtes landslov was the first state law covering the whole of Norway, issued during the reign of Magnus VI of Norway between 1274 and 1276. It remained a key section of Norwegian law until Christian V of Denmark issued the Norwegian Code in 1688.
The Forsaringen is an iron ring from the door of the church at Forsa in Hälsingland that carries a runic inscription listing fines, with the penalty doubling for each repeated offense. It is considered the earliest written law from what is now Sweden and has been dated to the ninth or tenth century.
Christianity, made the official religion of Norway by Olaf Tryggvason in the eleventh or twelfth century, introduced new legal tests such as the Járnburdr, a trial by fire, which the church later abolished. The church also abolished slavery and accelerated the shift toward monarchical rule, while monks took over the task of writing down the laws that lawspeakers had previously memorized.