Short answers, pulled from the story.
A housecarl was a free, paid manservant or household bodyguard in medieval Northern Europe, originating among the Norsemen of Scandinavia. The Old Norse term húskarl literally means "house man", and housecarls were distinguished from thralls (slaves) by being voluntarily in service. In England, they served as royal bodyguards, tax collectors, and soldiers.
The Witherlogh, also called the Lex Castrensis, was the legal code that governed Cnut the Great's housecarls in England, as described by the 12th-century Danish historian Svend Aggesen. It regulated seating at the king's table by rank and war skill, set punishments ranging from public shaming for minor offences to outlawry and death for murder or treason, and established a tribunal called the Huskarlesteffne to settle disputes. Because Aggesen wrote more than a century after Cnut's reign, it is uncertain whether the code accurately reflects Cnut's time.
Royal housecarls were funded by a dedicated tax and paid monthly wages in coin, as recorded by Saxo Grammaticus. Florence of Worcester called them solidarii, or "salarymen", and William of Malmesbury called them stipendarii, meaning "paid men". A housecarl could leave the king's service on only one day a year, New Year's Eve, when Scandinavian kings traditionally gave gifts to their retainers.
The Domesday Book, compiled after the Norman Conquest of 1066, records only thirty-three landholding housecarls across all of England, and those estates were described as small. Despite receiving monthly wages, most housecarls did not hold significant land grants from the crown.
The housecarls of Harold Godwinson formed the backbone of his army at the Battle of Hastings, positioned in the centre around Harold's standard and probably in the front ranks of both flanks, with the fyrd militia behind them. The Bayeux Tapestry depicts them as mail-clad footsoldiers wearing conical nasal helmets and fighting with two-handed long axes. After Harold was killed, the housecarls continued fighting until the last man fell, honouring their oath to him.
Historians have disagreed on this question for over a century. Charles Oman's 1885 work argued their main advantage at Hastings was esprit de corps, a view that influenced many later accounts. Historian Nicholas Hooper later argued that housecarls were not clearly distinguishable from Saxon thegns and should not be considered a defined military elite, though he allowed they may have had more uniform training and equipment than the average thegn.