Short answers, pulled from the story.
Mariam-uz-Zamani was born Harkha Bai, a Rajput princess and the eldest daughter of Raja Bharmal of Amer. She married Emperor Akbar in 1562 CE and received the title Mariam-uz-Zamani after giving birth to Jahangir in 1569 CE. She is described in the Fatehpur Sikri Chronicles as the first and last love of Akbar.
The tomb is in Sikandra, a suburb of Agra, directly beside the tomb of Emperor Akbar in the direction of Mathura. Mariam-uz-Zamani is the only wife of Akbar to be buried close to him.
Her son Jahangir commissioned and built the tomb between 1623 and 1627 CE, after her death on the 19th of May 1623.
The misidentification began with visitors to her residence at Fatehpur Sikri who believed a painting there depicted the Annunciation, and assumed from her name Mariam that she was Christian. The court historian Abul Fazl made no mention of a Christian wife, and the Mughal chronicle Khulasat-ut-Tawarikh explicitly identifies her as the daughter of Raja Bharmal. Edmund Smith had her crypt opened to investigate and found no trace of a cross.
During British rule the mausoleum was used as a printing press for an orphanage and then as the location of the Government Press. After the Press moved to Allahabad, factories were set up inside with partitioned walls added. Following the India-Pakistan partition, the building housed Sindhi refugees. White plaster applied during British rule covered much of the original decorative surface.
The tomb lacks a dome entirely, placing it in a rare category of Mughal tombs without one. It also has a functional rear entrance rather than a decorative dummy, making the structure identical from front and back. The original baradari on the site dated to 1495 AD and was built during the reign of Sikander Lodi before being converted into the mausoleum.