I have no further information on Hannah Robinson.Just too many Robinsons and variant spellings of the surname.
The following sources will help to answer the other questions:
TAG, vol. 168, pp. 193-205
Mayflower Families through five generations (Stephen Hopkins), pp. 30, 107-110
NEHGS, Volume 43: "Northrup Genealogy", pp. 242-243.
Northrup, A. Judd. "The Northrup-Northrop Genealogy"NY: The Grafton Press, 1908.
Vital records in England and Scotland are dicey before 1600.There was no requirement for the keeping of vital records until around 1540.At that time, Henry VIII of England and Francis I of France decided they needed to require them, probably because of taxation and war.
In England, there was mixed compliance at first.By 1600 or so, compliance was much greater, except in the case of Catholic families.However, many of the records were used to set fires in fireplaces, ovens, etc. and thus were destroyed.
Some researchers have managed to find vital records embedded in court cases and land records.Unfortunately, many of our ancestors did not own land and had no reason to go to court.