She is not a muslim and her parents don't live in Iran. Her father is dead and her mother lives in Chicago. Her mother is 87 years old.
Yes she was born in Iran, but her parents were Americans working overseas. Her father, a pathologist and geneticist, ran a hospital for children in Shiraz in 1956 as part of a program where American physicians and agricultural experts sought to help developing countries' health and farming efforts. When she was five years old, the family moved to London for a year, later moving to Chicago in 1963.
I just did a web search and it looks like you are correct (I haven’t checked her family’s background as yet).
Note that the sources of information in the post are the mentioned email and the web page listed after each statement or group of statements.
Your scrutiny is much appreciated - please keep it up.