Short answers, pulled from the story.
Humayun's tomb was commissioned by Empress Bega Begum, Humayun's first wife and chief consort. Construction began in 1565 and was completed in 1572, at a cost of 1.5 million rupees paid entirely by the Empress.
The tomb was designed by Mirak Mirza Ghiyas, a Persian architect brought from Herat in northwest Afghanistan and selected by Bega Begum. Ghiyas died before the structure was finished; his son, Sayyed Muhammad ibn Mirak Ghiyathuddin, completed it.
Humayun's tomb was the first garden-tomb on the Indian subcontinent and the first Indian building to use the Persian double dome on a high neck drum. It was also the first structure in India to use red sandstone at such a scale, and it set the precedent for later Mughal royal mausoleums, including the Taj Mahal.
Humayun's tomb was declared a UNESCO World Heritage Site in 1993. This designation prompted a major restoration by the Aga Khan Trust for Culture and the Archaeological Survey of India, completed in March 2003.
There are over 100 graves within the entire complex, earning it the name Dormitory of the Mughals. They include the graves of several later Mughal emperors such as Jahandar Shah, Farrukhsiyar, Rafi Ul-Darjat, Rafi Ud-Daulat, and Alamgir II, as well as Dara Shikoh, the son of Emperor Shah Jahan.
The last Mughal emperor, Bahadur Shah Zafar, took refuge at Humayun's tomb during the Indian Rebellion of 1857, along with three princes. He was captured there by Captain Hodson and subsequently exiled to Rangoon.