Olaf Haraldsson holds the title of Rex Perpetuus Norvegiae - eternal king of Norway. Technically, all Norwegian monarchs since the 12th century has held Norway as a fief to this long dead king.
Harald Finehair had many children. So many in fact that Harald Sigurdsson (Leo Suter) and Olaf Haraldsson (Jóhannes Haukur Jóhannesson) were both of his descendants, not by their shared mother as one might expect but by their different fathers who were descendants of different sons of Harald Finehair. They were 3rd cousins once removed in addition to being half brothers.
In this series the characters that are Norse refer to themselves repeatedly as 'Vikings'. Norse peoples did not refer to themselves as Vikings. In fact, it is not a term for a people at all, but rather, describes an action, usually referring to Norse people who went Viking, that is, raiding and seeking riches through conquering other peoples.
According to the Icelandic sagas, Canute (Bradley Freegard) was the great-great-great grandson of Ragnar Lothbrok through his father Sweyn.
The double "a" in "Haakon" is pronounced like the "ou" in "ought". The same goes with the "å" in "Kåre". Double "a" and the letter "å" is pronounced the same in Norwegian, with double "a" being more archaic spelling. In old Norse the sound is spelled with an "á". It does not occur in Icelandic.