I extracted the following from the online Webster Dictionary. It's interesting to see how all these words were transformed from Latin/Greek/Old High German/Middle English to the current English words.
Note: I know that this does not exactly answer your question, since you actually want to know if the words derived from words with other meanings. But I think that having the full list of originating languages here may be useful as other answers to your question may refer to it.
DAUGHTER
Middle English, doughter, from Old English dohtor; akin to Old High German tohter daughter, Greek thygatēr
First Known Use: before 12th century
SON
Middle English sone, from Old English sunu; akin to Old High German sun son, Greek hyios
First Known Use: before 12th century
AUNT
Middle English, from Old French ante, from Latin amita; akin to Old High German amma mother, nurse, Greek amma nurse
First Known Use: 14th century
UNCLE
Middle English, from Anglo-French, from Latin avunculus mother's brother; akin to Old English ēam uncle, Welsh ewythr, Latin avus grandfather
First Known Use: 14th century
MOTHER
Middle English moder, from Old English mōdor; akin to Old High German muoter mother, Latin mater, Greek mētēr, Sanskrit mātṛ
First Known Use: before 12th century
FATHER
Middle English fader, from Old English fæder; akin to Old High German fater father, Latin pater, Greek patēr
First Known Use: before 12th century
COUSIN
Middle English cosin, from Anglo-French cusin, cosin, from Latin consobrinus, from com- + sobrinus second cousin, from soror sister — more at sister
First Known Use: 13th century
NEPHEW
Middle English nevew, from Anglo-French nevou, neveu, from Latin nepot-, nepos grandson, nephew; akin to Old English nefa grandson, nephew, Sanskrit napāt grandson
First Known Use: 14th century
NIECE
Middle English nece granddaughter, niece, from Anglo-French nece, niece, from Late Latin neptia, from Latin neptis; akin to Latin nepot-, nepos grandson, nephew
First Known Use: 14th century
Reference:
http://www.merriam-webster.com
Best Answer
Yes, in General American English, the descriptive label for the grandchildren of your great-grandparent that are not your parents or aunts/uncles (or children of one's cousin) is 'first cousin once removed'.
But how you address them is really not settled or commonly agreed upon in the US. It all depends on your family's patterns, how close you all are, etc.
Using 'uncle so-and-so' or 'aunt so-and-so' for such a person would be similar to calling any friend or person in one's parent's generation the same, that is, some people do it, some don't. Also, this kind of calling is probably only for children – as they get older, they'll probably call them by their first name. (Of course, the older generation will probably only use the younger person's first name in any case.)
So feel free to use it if all parties are comfortable with it, but I would say it is not terribly common but that could be because the incidence of knowing well one's first cousin once removed isn't that common.