On the name issue, common nicknames in the last century for Margaret include: Maggie, Marg, Margie, Peggy, Daisy, Meg, Midge, Peg, Peggy, Rita, Margery, Marge, Margie
"Magdalene" is another form of Margaret, and shares many of the same nicknames.
"Polly" was a common nickname for Mary
Someone named Mary Margaret or Mary Magdalene (both VERY common names for girls from about 1700 to 1950) could be referred to by most of those names listed above. Nor was it uncommon for record keepers to refer to the same person by different nicknames names on different documents. (And different spellings are ubiquitous.)
All of those names are so common, as is John, that it's hard to use them as evidence, though.