Washington Green Falkner

'Wash' Falkner (my 2nd great grandfather) was born 1 Sep 1858, Alert, Sandy Creek Township, Franklin Co., North Carolina and died 26 Sep 1924 in the same location and was buried in the family burial plot nearby.  Cause of death was heart failure.  He fell in the yard and died in 5 minutes, according to his death certificate.  His wife was daughter of Albert Green Pernell and Henryetta Christmas Duke Pernell, Narcissia Geneva Pernell, born 7 Feb 1858, Sandy Creek Township, Franklin Co., North Carolina and died 23 Jul 1925 in Henderson, Vance Co., North Carolina, which is the location of the closest hospital, and is also buried in the family burial plot next to her husband, Washington.
Their children were all raised at Alert, Sandy Creek Township, Franklin Co., North Carolina

• Albert Green Falkner (1876-1950) My great grandfather
• Charles E Falkner (1881-1901)
• James Earnest Falkner (1884-1956)
• Richard Cleveland Falkner (1886-1959)
• Elizabeth C L Falkner (1888-1986)
• Tollie Furman Faulkner (1891-1975)
• Wiley Falkner (1891-1950)
• Ada S Faulkner (1893-1965)
• William W Falkner (1895-1974)
• Percy Jessie Faulkner (1899-)
• Gussie G Falkner (1899-1943) 
• Ollie Thomas Falkner (1900-1972)

Elizabeth Virginia Falkner

Not much is known about my third great grandmother Elizabeth Falkner.  I have not found any evidence of marriage and have been told by family members, she was in fact never married, but raised seven or more children.  While looking at the pieces of accumulated information it is hard to distinguish what is correct. Elizabeth was born in Sandy Creek township, Alert, Franklin Co., North Carolina on 20 Dec1833 as found in the Falkner family bible passed down to a first cousin.  The information was hand written and hard to read. She died 27 Nov 1912, in the same community. Evidence of this was determined by the tombstone placed on her grave in the Faulkner Family Cemetery and her death certificate, which I found on ancestry.com.
Looking at other documents, such as census reports can be very confusing, but with investigation of the documents as a whole can lead you to the truth.  However, the more I look at census reports for Elizabeth Falkner, the more confusing they become.  Here is what I found:

1860 census
Jinny Falkner  age 65  (maybe Elizabeth's mother)
Elizabeth Falkner age 25
James Mosley age 14
Washington Mosley  age 7
William Mosley  age 3
Lucy Mosley  age 6
Mary Mosley  age 6 months
Jane Mosley age 22

1870 census
Elizabeth Falkner age 36
Washington Falkner age 15 (name changed since 1860)
John H Falkner age 18 (not on 1860 census)
William Falkner age 14 (name changed since 1860)
Charles Falkner age 8
Ernest Falkner age 5
Sallie Falkner age 1

1880
Elizabeth Falkner 47
Ernest Falkner 15
Sally Falkner 12
Gertrude Falkner 9

1900
William H Falkner age 43 (listed as head of house)
Elizabeth Falkner age 66

Questions:
Are the Mosley children in the 1860 report Elizabeth's?  James is probably not her child because of his age.
Where does Jane Mosley fit in this report?  Elizabeth did have a sister named Jane Malon Falkner born in 1838.
Which name is correct for Washington and William?  Is it Falkner or Mosley?

Theories:
1.  Elizabeth was never married and all of her children were illegitimate. James in 1860 was her stepson.
2.  Elizabeth had a sister that married a Mosley and when the sister and husband died unexpectedly, Elizabeth stepped in to take care of the children and eventually change the name from Mosley to Falkner.
3.  Elizabeth was a kind-hearted young woman and dedicated to raise these orphaned children.

Where does this leave me? I'm not quite sure.  Am I a Faulkner or a Mosley?