Short answers, pulled from the story.
The term ringkvinna described an unmarried woman who inherited the position of head of the family. She received all tasks and rights associated with that leadership role during the Viking Age and continued into the Middle Ages.
No law texts mention the concept after the late thirteenth century. The practice vanished completely by the end of the 1200s following Christianization across Scandinavia.
Only daughters or sisters of dead men could inherit the actual head of family position. All other female relatives such as paternal aunts, nieces, and granddaughters were named odalkvinna but held no complete set of powers.
Upon marriage her rights transferred directly to her husband immediately upon union. She lost the ability to demand fines for family member slaughter after wedlock and the transition marked the end of her independent legal standing.
Ringkvinna appears primarily in the Icelandic Grágás legal code. It also features within Norwegian Frostating laws and Gulating laws with similar phrasing across regions.