In To Kill a Mockingbird, who is responsible for teaching Calpurnia standard English?Also, why doesn't Calpurnia speak standard English when she is...

The reader cannot know more than what is written in the book (because there's no "reality" elsewhere), but one can presume that since Calpurnia has been with the Finch family ever since the death of Jem and Scout's mother (and perhaps even before), she is fully immersed in white culture. Atticus, being the responsible father that he is, would have of course chosen Calpurnia by the criteria of her level of education and not just her housekeeping or cooking skills. She has, after all, taken on the role of a surrogate mother for his children and seems to amply "fill the bill."

Calpurnia's "double-talk" is her strategy to be a part of both worlds. If a Negro took on "white man's talk" he or she would be critized by both the white and black communities for not respecting his/her station in life or "place."  There have even been psychological studies done concerning this in comparison to the comportment of prisoners of war who adopted a demeaning manner to avoid further persecution.