Short answers, pulled from the story.
Indo-Islamic architecture began in earnest with the establishment of Delhi as the capital of the Ghurid dynasty in 1193. The earliest known mosque on the subcontinent, at Banbhore in Sindh, dates to 727, but sustained architectural development followed the founding of the Delhi Sultanate in 1206.
The Qutb Minar is a minaret and victory tower in Delhi, part of the Qutb Complex begun before 1199. Its original four stages reach 73 meters, with a final stage added later. Its closest parallel is the 62-metre Minaret of Jam in Afghanistan, built around 1190.
Bengal Sultanate architecture, spanning 1352 to 1576, relied almost entirely on brick because stone had to be imported. Its distinctive features include a slightly curved cornice, large round decorative corner buttresses, carved terracotta ornament, and a preference for multiplying domes rather than enlarging a single one. The Sixty Dome Mosque at Bagerhat, completed in 1459, has 26 doors designed to improve ventilation in a high-rainfall climate.
Shah Jahan built the Taj Mahal as a mausoleum for his wife Mumtaz Mahal, who died in 1631. It drew on the garden tomb traditions developed by earlier Mughal emperors and became the most recognized example of Mughal architecture.
Indo-Saracenic architecture is a style developed mainly from the 1840s until Indian independence, designed largely by British and European architects. It applied Islamic and Mughal decorative features to buildings whose structural forms followed Western models, including railway stations, courts of justice, and hotels. It is one of the main channels through which Indo-Islamic architecture influenced modern Indian, Pakistani, and Bangladeshi building.
The Gujarat Sultanate, independent between 1407 and 1543, was notable for its inventive use of minarets, often in pairs flanking the main entrance with elaborate stone carving. Gujarat builders drew on local Maru-Gurjara temple carving traditions and introduced elements including ornate mihrabs, jali perforated screens, and chattris - pavilions topped with cupolas - that later appeared in Mughal architecture.