I have that Edmund was born about 1738 in Albemarle Parish, Surry County, VA. The 1738 is an estimate, since his first child, Susannah, was born 12 Mar 1755. (The birth is recorded in the Parish Register of Albemarle Parish.)
Edmund appears to be the son of Charles and Mary Gilliam of Surry County, VA. Though we do not have a Will for Charles, a deed does mention son, Edmund.
21 Oct 1757, Charles Gilliam of Sussex County, conveyed to son, Edmund Gilliam, of Sussex County 100 acres in Sussex County. [Note Sussex County was carved out of Surry County, VA] This date corresponds with the birth of Edmund's children in Albemarle Parish. It appears he moved to NC after 1768.
The Inventory of Charles mentions Ralph Magget. This Ralph is believed to be Ralph Magee, the father of Sarah who married Edmund. By the way, the godparents for Susannah above is Ralph Magee. This would make sense if he was her grandfather!
Will Book 9, page 134 Inventory date 14 Aug 1767 Adminstrator, Patty Gilliam Signers: Hinchea Gilliam, John Dunn, Ralph Magget [Magee?]
This brings up your other question regarding name spelling. Since English spelling was not standardized at this point and because many were illiterate, we see many different spellings. Often people could not spell their own names and signed wills and deeds simply with an X or a mark. Also, if an area was settled by a particular people group, spellings tended to look like the language of that people group. For example, my James Gilliam when he settled in Powhatan County, VA (a county settled by French Huguenot refugees) mysteriously gained an "U" in his last name becoming Guilliam. People have taken this to mean that James was French and many incorrect things have been posted regarding French ancestry for this line. Anyway . . . my point is . . . never put too much interest into a particular spelling and always explore variant spellings, at least in the early days.