Short answers, pulled from the story.
Yusuf Adil Shah established the Sultanate of Bijapur in 1490 as a de facto independent state. He rose through the ranks of the Bahmani Sultanate to become governor of the province of Bijapur before declaring independence when the Bahmani state began to crumble in the late 15th century.
The Vijayanagara Empire was decisively defeated at the Battle of Talikota in 1565, resulting in the capture and beheading of the ruler Rama Raya. The subsequent sacking of the capital city lasted for five to six months and prompted a massive emigration of the population to Bijapur.
Ibrahim Adil Shah II is remembered for composing poetry and playing music, including the Kitab-i Nauras collection of Deccani musical poetry. He commissioned the Ibrahim Rauza complex which was completed in 1626 and combined a mosque and a mausoleum to set a new standard for Deccani architecture.
The Gol Gumbaz features a massive dome that was the largest in the Islamic world at the time of its completion and creates a unique acoustic phenomenon known as the whispering gallery. Mohammed Adil Shah ruled from 1627 to 1656 and the dome was nearly finished when he died in 1656.
The Sultanate of Bijapur came to an end on the 12th of September 1686 after Mughal forces led by Aurangzeb began a siege in April 1685. The last sultan Sikandar Adil Shah was only four years old when he ascended the throne in 1672 and was sent into Mughal captivity after the fall of the capital.