Fausett:
The Fausett name likely originates from Northern England and is considered a topographical name or toponymic surname deriving from the Anglo-Saxon Old English (pre 7th Century) word’s “fah” and “side”, widely interpreted as “brightly coloured”, “variegated”, or “flowery” on the “side” or “slope” of a hill.
Another possible origin of the Fausett name….
“Forset: (Old Norse forseti, a judge) has given surname to Forset, Fawcett. The title was used only in Northumbria, and the office was changed and lost its Scandinavian designation after the complete reduction of the North by William. It occurs in Domesday.”
See: The Danes in Lancashire and Yorkshire By S. W. Partington / British Family Names–Their Origin and Meaning . . ., https://mythology.wikia.org/wiki/Forseti
Foster:
The Foster Families in America got their heritage in England about 1066 AD after the Battle of Hastings when William the Conqueror knighted a 16-year-old young man (his nephew) Richard de Forestarius and gave to him and his posterity the northern part of England known as Northumberland. The Forster’s surname evolved and the first son’s in each generation inherited the land, titles and the money.
The second and additional sons eventually became known as Foster. The many Foster families spread southward in England and by the early 1600’s were going abroad to establish homes and lands of their own in the English Empire. Some were Knights of the noble class and had occupations as, soldiers, merchants, landowners, physicians, ministry and the trades. – (source)
Nuñez Origin:
medieval form Nunes, derived from the name Nunnus + suffix -ici-.
Nuñez is a patronymic surname. This means that a few letters were once added to the name of a paternal ancestor. In this case, Nuñez comes from the given name Nuño, accompanied by the traditional patronymic suffix – ez. The personal name Nuño is of uncertain derivation. It may be from the Latin nonus, meaning “ninth”; nunnus, meaning “grandfather”; or nonnus, meaning “chamberlain” or “squire.”
Guillén Meaning and Origin:
Spanish (Guillén): from the personal name Guillén, Spanish equivalent of William.