Hi David, I really haven't been able to tie this family to our family, although the names are familiar ... we did have a Hannah Falling (or Fallin) and sometimes the name was spelled various ways ... like Fawling.
I don't know about Major John Downing and Annie BeeHunter (a Cherokee woman) or supposedly Hannah Fawling was a full blood Cherokee woman too ... but I am pretty sure our Hannah Fallin daughter of Redmond Fallin wasn't a full blood and if half Indian, maybe ... but doubtful, but if part Indian ... definitely not Cherokee, our Indian admixture if it happened at all would have been on the coast and in the 1600's and more than likely would have been with some sort of "Powhatan" group. Although ... I saw a copy of a copy of an old newspaper article that said something about the Fallin Family Farm having been raided by the "Saponi" Indians and one of the Fallin girls was taken away and returned "with child". But even THAT story seems unlikely. I guess anything could happen though, it's just UNPROVEN so far ... I'll be doing a DNA thing later on next year and we'll find out more.