Short answers, pulled from the story.
Alwin served as Sheriff of Warwickshire at the time of the Norman Conquest in 1066. His son Thorkell managed to keep his family's status after the invasion by forces from France.
Sir John de Arderne established a primary estate near Solihull at Park Hall in Castle Bromwich by the 14th century. Another branch of the family operated out of Underbank Hall in Stockport during the 1500s.
Edward's great-grandson Robert died unmarried without issue in 1643 ending the Park Hall male line. Edward Arden served as Sheriff of Warwickshire in 1575 while living at Park Hall.
William Shakespeare traced his maternal lineage directly to an Arden ancestor through his mother Mary. Edward Arden was the second cousin of Mary Arden who became mother to William Shakespeare.
Modern scholars note only four other families can trace their male line back to pre-Norman times like the Ardens do. The Berkeley family and Swinton family share this distinction alongside the Wentworth and Grindlay families.