B.J.'s Biggest Genealogical Conundrums

Date: [unknown] [unknown]
Location: [unknown]
Surnames/tags: Little Sears Batchelder

After 25+ years of researching, I still have some puzzling genealogical conundrums:

Elizabeth Little: who was her father? Her mother, also named Elisabeth Little, had four children but never married; it's not clear whether the children had the same father or not. On various trips to Scotland, I've searched local archives from Hawick (near where the family lived most of her life) to Inverness (her mother was born in Farr, on the north coast of Scotland). The kirk session records don't seem to exist for the parish she was born in; I've searched both the established church kirk session records for surrounding parishes as well as any nearby Free Church kirk session records held in Edinburgh and Hawick. As of 6 March 2023, DNA has not been useful in determining her father.

Who was John Sears? Where did he come from? John T. Sears appears in the Marblehead/Danvers MA area about the time of the War of 1812. He married Betsy Wilkins in 1815, had two children with her, then died on a voyage to the West Indies.

Nancy Batchelder: who were her parents? Her death record says her father's name was John and she was born in Billerica MA but that information hasn't produced any matches.