Regarding "parishes", regard them simply as being a sub-division of a County.
Depending on their locations, some rural parishes cover a substantial area, so include villages, townships etc.
Others in towns and cities, cover relatively small areas.
They are generally the areas covered by a (group of) church/es (Kirks).
In this era up to 1854, it was mainly Baptisms and Banns (proclamations) of forthcoming marriages that were "officially" recorded in the Parish Registers, with the Birth Date and the Marriage Date respectively almost being after-thoughts.
The mother was all too often totally omitted from the Baptismal record!
With the introduction of Statutory Registration in 1855, the Registration Districts tended to cover the same or similar areas; and also tended to use the old parish names - BUT not always.
Regarding Margaret giving her marital condition as "Widow", back in those days, it was also used occasionally as a euphemism for being separated.
In one case, I found the husband living "round the corner", so close that the "widow" almost certainly knew that he was alive etc.
Reading that 1871 Census extract, the last two entries normally would be read that they are "GrandDaughters" of the nearest Household "Head", ie of (Margaret) Harper.
There is a chance that the Head's First Name is given on the Scanned IMAGE of the Census Document; but erroneously omitted in the transcription to the Search Index.
I have seen thar occur where the original Marriage Record was complete with the Bride & Groom's Names etc, very clearly written, yet the Search Index totally omitted the Groom's Names - a "one-sided marriage"!
Regarding Margaret's Birthplace, I would tend to trust the Censuses particularly if they show consistency.
Keep on mind that obituaries written usually by non-relatives and in this case overseas and far removed in time and space from her actual birthplace where-ever that actually was.