The following is information I came across regarding the Applegate family and the Wall family. The Applegate family source of information is from volume iii, page 15 of "Historical and Genealogical Miscellany: Data Relating to the Settlement and Settlers of New York and New Jersey", by John E. Stillwell, M.D. It is under the section titled "Applegates of Ocean County". The excerpt does not mention the parentage of, or the relationship between Benjamin, William, Samuel or Daniel Applegate:
Benjamin, William, Samuel and Daniel Applegate were among Jerseymen who came to Western Pennsylvania about the year 1766, and settled on a neck of land, called "The Forks", lying between the Monomgahela and Younghiogheny Rivers, about sixteen miles south of Pittsburgh. It was also known as the Jersey settlement.
Benjamin Applegate, born 1725, died May 21, 1823; married Rebecca, supposed sister of Walter and James Wall.
William Applegate married ........They removed to Missouri, except Robert Applegate, who remained.
Daniel Applegate married ............
The Wall family information is from the same author and title of book but volume v, pg. 233, under Wall of Monmouth County, N.J., Miscellaneous Notes:
Walter and James Wall, reputed sons of Humphrey Wall, came from New Jersey, and settled on a neck of land, called "The Forks', lying between the Monongahela and the Younghiogheny Rivers, about sixteen miles south of Pittsburgh, in Alleghany County, Pa. For years this locality was known as The Jersey Settlement, by reason of its numerous settlers from New Jersey, especially from Monmouth County. In 1769, after having cleared land and built houses, they brought their families. The records of these Walls were destroyed, by accident, many years ago, and I am strongly inclined to believe that instead of Walter and James Wall being the sons of Humphrey Wall, they were the children of James Wall, as appears from the following will:
1750-51, Mch. 13; will proved Apr. 4, 1760, to which he made his mark. James Wall, sick, of Middlesex County, mentioned: wife; four daughters:Martha, Rebecca, Abigail and Neomia, each -L- 10; two sons, Walter and James, the residue of his estate. All of children were minors. Executors: Friends, John and Joseph Story.
Walter Wall married Alice, a sister to Benjamin Applegate.
James Wall, the brother of Walter Wall, married Elizabeth Vaneman.
It is said Rebecca Wall, sister of James and Walter Wall, Married Benjamin Applegate born 1725; died May 21, 1823, whose sister Alice Applegate married Walter Wall.
Allen Wall, of Washington, D.C., has a complete list of their descendants. [Stillwell's vol. v, was originally published in 1932. End of excerpt.]
Since there are nobirth/death dates for Stillwell's Alice Applegate who married Walter Wall, I can't tell if she is the same as your Alice Applegate but thought you might me interested in theApplegate/Wallconnection.