Is it true that "illegal" (as in not legal...er right) children from the king were added ´fitz´ to their names? So ´fitzwilliam´ would be a family line from the king

Yes... as far as I'm aware, 'fitz' was the Norman word for 'son' and entered the English language after the Norman Conquest. However, the English (showing the usual respect for our French neighbours) adapted the word as an insult, meaning 'illegitimate son', as in Fitzroy/'Fitz Roi'.... 'son of the French King'. It came to stand for an illegitimate branch of the royal line.

Perhaps this accounts, in part, for Darcy's regal air?!

(By the way, I'm a new member to this site, so probably shouldn't be posting answers to such interesting questions as I'm sure there's a greater authority on hand. Apologies for such effrontery!).

Sarah B