Short answers, pulled from the story.
The present-day structure of the Agra Fort was completed in 1573 under the orders of Akbar. The original brick fort known as Badalgarh stood in a ruined condition when Akbar began renovations from 1565.
Architects laid the foundation with bricks in the inner core while covering external surfaces with red sandstone from Barauli area Dhaulpur district in Rajasthan. Shah Jahan later rebuilt parts of the fort using white marble instead of red sandstone.
This octagonal building surmounts the largest bastion of Agra Fort on the riverside facing East. It was originally built of red stone by Akbar who used it for jharokha darshan and sun worship every day at sunrise.
Shah Jahan spent eight years from 1658 to 1666 AD imprisoned within the Muthamman Burj complex after being placed under house arrest by Aurangazeb. This period followed his defeat in a bloody war of succession.
In 1983, the Agra fort was inscribed as a UNESCO World Heritage Site because of its importance during Mughal rule. The site won the Aga Khan Award for Architecture in 2004.