The song Emily is humming when she returns from her errands is "Greensleeves" (also known as "What Child Is This?" --a popular Christmas Carol).
Just after the shot of the church's interior, several times the viewer hears a male and female voice say the words "dementia praecox". Dementia Praecox is an archaic nineteenth century term for the mental illness psychiatrists now call Schizophrenia. Dementia Praecox is Latin for very early dementia, and the term was appropriate to nineteenth century psychiatrists since the disease onset of Schizophrenia is often in a person's late teens or early 20s.