Whether Richard Hail and Elizabeth Edmondson are parents of this Francis is just conjecture, based only on Richard's will mentioning a son Frank. The Francis Hale remaining in the Virginia census could be son of Richard's brother Lewis, leaving Frank to have gone to Indiana. Numerous DNA matches between descendants support this connection. It's still possible Richard Hale of Bedford is only Francis Hale's uncle as Francis was a common givenname in this line.
I believe Francis and Caty Hale were in the part of Knox that became Gibson County because Caty Hale remarried there. However some other Hales were in Sullivan County very early. These Hales came from Grayson Co, VA. Stephen Clark Hale and Anna Lyon Howard had a son named Francis. Other Hales in Sullivan: Martin, Noah were sons of Richard Hale and Elizabeth Stone who moved from Grayson Co, VA to Sullivan after 1820. A Joshua Hale (b.1780-1790) is in Sullivan by 1820. A photo of Noah Hale strongly resembles Oliver Hale.