Short answers, pulled from the story.
Mughal painting is a style of miniature painting originating in the Indian subcontinent during the rule of the Mughal emperors, spanning the 16th to 19th centuries. It reflects a combination of Indian, Persian, and Islamic artistic traditions, used as book illustrations or as single works kept in albums called muraqqa.
The foundational figures of the Mughal atelier were the Persian masters Abd al-Samad and Mir Sayyid Ali, whom the emperor Humayun brought to India after his exile at the Safavid court of Shah Tahmasp I in Tabriz. A third master, Dust Muhammad, a disciple of Kamāl ud-Dīn Behzād, also contributed to the early formative period.
The Hamzanama was an illustrated manuscript produced between 1562 and 1577 in the court of Akbar, comprising 1,400 cotton folios each measuring approximately 69 by 54 centimetres. It was the project that forged a unified Mughal style by bringing together artists from Iran and different parts of India, transforming the flat decorative approach of Persian painting into scenes with believable space and three-dimensional figures.
European influence entered the Mughal atelier through Western prints available at the court from the time of Akbar, and deepened under Jahangir, who received gifts of oil paintings from the English Crown including royal portraits. Jahangir encouraged artists to adopt single-point perspective, and equestrian portraiture became popular from the 17th century onward as a borrowing from Western models.
Yes, women artists worked in the Mughal atelier and contributed to major commissions. The Gulshan Album included work by at least three women artists. Sahifa Banu made portraits and copies of compositions by celebrated masters, while Ruqaya Banu, Nuri Nadira Bano, and Nini produced copies of European engravings and prints in their own style.
Aurangzeb, who reigned from 1658 to 1707, was not an enthusiastic patron and largely withdrew from commissioning paintings around 1668. There was a brief revival under Muhammad Shah, who ruled from 1719 to 1748, but by the reign of Shah Alam II the tradition had declined significantly. Many Mughal-trained artists left the imperial workshop for Rajput courts, contributing to regional styles called post-Mughal or provincial Mughal.