I don't know the origin of the name Ables but through my research of my Abel surname, I have found all of the spelling variatians that you listed, sometimes even within the same family.My father spelled his name "Abel" but his brothers spelled it "Ables".
I think the name may have originally been spelled "Abel".I remember when I was a child there was a tendency for neighbors to refer to my family as "Ables" and to my dad as "Sam Ables".My Abel folks came from South Carolina to Alabama via East Tennessee (Knox, Monroe, McMinn Counties)in the early 1800's.There was another group names "Abel" in Lincoln County, Tennessee in early 1800's.Several "Ables" researchers in Mississippi trace their ancestry to an "Abel" in South Carolina.
The name, "Abel" of course is biblical. In Hebrew, Abel was a meadow.The name, "Abel" can be found in England, Ireland, Scotland, Germany, Norway and Russia. I have not found any reference to an Abel coat of arms.