Short answers, pulled from the story.
The word housecarl enters the English language through the Old Norse term húskarl, which literally translates to house man. This specific linguistic root distinguishes the role from servile classes like thralls or slaves in medieval Northern Europe.
Housecarls in Norway were members of the king's hirð, an institution traceable back to the ninth century. The Heimskringla and Konungs skuggsjá texts make explicit the link between a leader and his bodyguards during this period.
In the 1060s, royal housecarls were paid with Norwegian coins according to Icelandic sources. A special tax provided pay in coin to the royal housecarls monthly according to Saxo Grammaticus.
As combatant retainers, the term came to acquire a specific sense of men serving in a hirð or drótt. This meaning appears on the Turinge stone where Þorsteinn may have commanded the retinue of Yaroslav the Wise.
Murder of another housecarl resulted in outlawry and exile whereas treason brought death and confiscation of property. Quarrels between housecarles were decided by a tribunal called the Huskarlesteffne in the presence of the king.