When Ethel is in the village, she stops and puts her basket down and there is woman and a pram behind her. In the next shot, she walks off and both the woman and the pram are gone.
For baby Sybil's christening, Tom assures Lady Mary that a Protestant is permissible as a godparent provided the other godparent is Catholic. This is true only since 1983. Before that time, canon law allowed for a non-Catholic to stand in as a proxy to an actual godparent who couldn't be present, but that proxy had to be selected by the godparent rather than by the child's parents.
Roman Catholics do not 'christen' their children-that is a Protestant term.
Babies are baptized into the Church, even in 1920.
Isabel, Edith and Violet discuss The Scarlet letter which Violet has never heard of. It was published in 1850 and very popular in America and England. It's very doubtful that an educated woman would have been unfamiliar with the book.