Short answers, pulled from the story.
Yusuf Adil Shah established Bijapur as a de facto independent state in 1490, after serving as governor under the Bahmani Sultanate. The kingdom became formally independent in 1518 when the Bahmani Sultanate finally collapsed.
Yusuf Adil Shah founded the Sultanate of Bijapur. His exact origins are disputed: historians have proposed he was a Georgian slave, a man of Persian or Turkmen origin, or even a son of the Ottoman Sultan Murad II.
Mughal forces under Aurangzeb besieged Bijapur beginning in April 1685. The siege concluded on the 12th of September 1686, when the sultanate was conquered and its last sultan, Sikandar Adil Shah, was taken into Mughal captivity.
The Battle of Talikota in 1565 was a decisive victory for a coalition of Deccan sultanates, including Bijapur, over the Vijayanagara Empire. The Vijayanagara ruler Rama Raya was captured and killed, the city was looted for five to six months, and the Raichur Doab was returned to Bijapur, allowing the sultanate to double its territory over the following years.
The Gol Gumbaz is the mausoleum of Mohammed Adil Shah, built in Bijapur during his reign. Its dome was the largest in the Islamic world when the structure was nearly complete at Muhammad's death in 1656.
The Bijapur school of Deccan painting was rooted in Persian miniature traditions and was characteristically baroque in style. Unlike North Indian painting of the same period, it avoided depicting battles and court events, instead favouring atmospheric, dreamlike fantasies.