] 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.

Yes, "fils" (pronounced "fiss" or "feess") is still the word for "son" in French today. Thanks for the info about "Fitz" - I never made the connection before!