Short answers, pulled from the story.
Hamida Banu Begum entered the world in 1527 within a family of Persian descent. She grew up as a devout Muslim surrounded by religious traditions while her father Shaikh Ali Akbar Jami served as a preceptor to Prince Hindal Mirza.
Hamida Banu Begum married the exiled emperor Humayun on a Monday in September 1541 at Patr in Sindh. Astrologers chosen by the Emperor determined this specific date for their union after he pursued her for forty days.
The couple reached Umerkot ruled by Rana Prasad who gave them asylum in that small town before arriving safely within Sodha Rajput territory on the 22nd of August 1542. Two months later early in the morning on the 15th of October 1542 she gave birth to Akbar.
Hamida used her influence to obtain forgiveness for state offenders on multiple occasions during Akbar's reign. Her most notable intervention came during the ouster of Mughal minister Bairam Khan when Akbar reached maturity in 1560.
Hamida took upon the case of her grandson Prince Salim during his rebellion against his father Akbar. She managed to bridge the gap between father and son through diplomatic efforts even though Salim had plotted and killed Abu'l-Fazl.