This is an interesting question but it's a little easier to understand if you live in the South. It is a longstanding custom among many Southerners to teach their children to call close friends and neighbors by their first names--with a "Miss" (or "Mister") preceding the name. Many men also preface a woman's name with "Miss," since Atticus often addresses the ladies in that manner. Since Stephanie Crawford, Rachel Haverford and Maudie Atkinson are longtime friends and neighbors, Atticus has passed on this custom to his children. Scout remembers it too late in the final chapters: When she meets Boo Radley for the first time, she addresses him as "Hey, Boo"; Atticus gently corrects her--"Mr. Arthur, honey," he says. (As a child growing up in 1960s Florida, I addressed many of my parents' friends by their first names--prefaced by a "miss," or in some cases "aunt." Today, I still have several friends whose children call me "Mister John.")
As for Calpurnia, this custom--especially in the 1930s--does not always apply to African Americans being addressed in the same manner. Negroes simply did not command the equal respect of white people, and employees (and especially black ones) were not usually called "mister" or "miss (or missus)" by their bosses. I imagine Atticus grew up calling his family's housekeeper "Cal" and Calpurnia" probably more out of love and familiarity than disrespect.
Interestingly, Miss Maudie Atkinson is not single: Born as Maudie Buford, she is apparently a widow who married a man named Atkinson. Nevertheless, the children still call her "Miss." Perhaps an even better question would be why Jem and Scout call their father "Atticus" instead of "dad" or "father." I don't believe this is ever explained in the book, but Atticus must have preferred that his children call him by the much more friendly, and certainly less formal, first name--just as they call Cal, who is considered a member of the family, by her first name. It could also be that the children don't know Cal's last name, since it is never revealed in the novel.