Short answers, pulled from the story.
Hamida Banu Begum was born in 1527 into a family of Persian descent. Her father was Shaikh Ali Akbar Jami, a Shia scholar known as Mian Baba Dost who served as a preceptor to Prince Hindal Mirza.
The marriage of Hamida Banu Begum and Humayun took place on a Monday in September 1541 at Patr, a town in the Sindh region. The emperor chose this location using his astrolabe to secure help from rival Shia groups during times of war.
Hamida Banu Begum gave birth to the future Emperor Akbar on the 15th of October 1542 in Umerkot. This small desert town was ruled by Rana Prasad, a Hindu Sodha Rajput who granted the couple asylum.
Hamida Banu Begum was reunited with her son Akbar on the 15th of November 1545. This event occurred after she had left her young son behind to accompany her husband to Persia and visit the shrines of her ancestor Ahmad-e Jami.
Hamida Banu Begum died on the 29th of August 1604, just a year before the death of her son Akbar. She was buried at Humayun's Tomb in Delhi, where her cenotaph stands alongside that of Dara Shikoh and others.