Hopefully, answers to your questions:
1. No, it is not a typo.He seems to have been pretty free with his age (along with many others of that time).I estimate from other info that he was probably born between 1823 and 1825. His parents, Joseph Badger and Evira C. Newman were married in March, 1822.Their children were Joseph Lawrence, Edwin Lafayette, William Haines, and Eloise (Ella).Edwin was born in 1824. William in 1827. I am unsure whether Joseph Lawrence or Edwin was born first.From a court case in 1846 about the division of property of their grandfather, Joseph Badger, after their grandmother, Ann, died, it lists Joseph (Lawrence) and Edwin as older than William and Ella and able to inherit directly (at least 18) so he couldn't have been born after 1828.In the Petersburg, VA 1840 census there is one male in the 15-19 age range (born 1821-1825) and no older males other than the father. Two males are listed in the 10-14 age range.
2. Badgers in Petersburg, VA:
Joseph Badger, first evidence in Petersburg in 1786, d. 1803 in Petersburg, VA (also reported in Massachusetts paper)
Married Nancy (Ann?) Shepherd 1786
Children: a. Mary Ann (b.abt. 1887, d. bef 1844)
b. Joseph (b. aft. 1791, d. 1841-1844)
Married Elvira Newman 1822
Children: Joseph Lawrence (c1823-25 -aft.1860)
Edwin Lafayette (1824-1896)
William Haines (1827-1907)
c. Harriet (abt. 1796, d. bef 1844)
d. William Henry (b.1798, d. 1879)
e. Edwin Hollingsworth (B. 1802, d. aft 1877)
Laurance is a name from his mother, Elvira Newman's family.Her sister was named Elizabeth Laurence Newman. His maternal great-grandmother was Elizabeth Lawrence Morgan.He had a Great-uncle named Laurence H. Wills. Also, his aunt Mary Ann Badger Dejernatt lived in Catawba County, NC. (Confirmed by some court papers they signed). According to Ruby Pruit, Joseph Lawrence Badger went to live with his aunt in Cabarrus County, NC after his parents died.In 1851, Laurence Badger, is listed as the editor of the Hornet's Nest in Charlotte, NC (which is next to Cabarrus County) and is later listed as J. L. Badger, editor of the Hornet's Nest who was born in VA and moved to NC; so this seems to indicate that this is the right person.He married twice and had one daughter.I believe Ruby Pruitt got much of this information from Alma Barclay, a descendant of his daughter.His wives were from Duplin County which could explain why he was living there in 1860.
3. Joseph Badger in Charleston, SC
Joseph, son of Boston artist, Joseph Badger
b. 1736, Boston - d. 1800 Charleston, SC
Married Rhoda Cox 1755 in Boston
Children: James b. 1757 in Boston, d. 1817, Charleston
Joseph b.1761 in Boston (Could this be the Joseph who appears in Petersburg, because he doesn't stay in Charleston)
Rhoda b. 1764 in Boston
Moved to Charleston, SC in 1766.Somehow linked to Jonathan Badger already in Charleston, SC.
(There is a Rhoda Badger who died in Charleston in 1782, but unclear whether this is Joseph's wife or his daughter.)
4. Also in Charleston was Daniel Badger, an artist who moved from Boston to Charleston in 1735.He is possibly the brother of Joseph Badger, the Boston artist according to MESDA.If so he would be the uncle of the Joseph who came to Charleston in 1766.He appears to have died in Ipswich, Boston around 1776. He had a son named John, who was also an artist.
James Badger, the son of the Joseph Badger who moved his family from Boston to Charleston had the following children:
a. Daniel b. 1786 in SC, d.1823, Charleston SC
Children: Lawrence, birth date or place not listed but probably in Charleston as his father was born, worked and died there.So it is unlikely that he was the Lawrence Badger who was born in VA and moved to NC.
b. Elizabeth Rhoda 1788-1865 m. George Ernest Hahnbaum
d. Katherine 1791-c1792
e. James Jr. 1793-1838 m. Mary Blaylock Bell
f. Margaret 1794 - ?
g. Rebecca 1796-1878
h. Martha 1800- ?
i. Harietta bef 1801 - ?
j. William Sanders 1806-1813
You can contact me directly if you wish.