Short answers, pulled from the story.
Timurid architecture refers to the building tradition of the Timurid Empire, which ruled from 1370 to 1507 across most of Iran and Central Asia. It is characterized by grand scale, lavish tilework, double-shelled domes in an onion shape, and sophisticated geometric vaulting. The style reached its greatest sophistication in the first half of the 15th century.
Timurid builders used three main tile techniques: banna'i tiling for geometric patterns and Kufic inscriptions at low cost, tile mosaic for more expensive curvilinear floral designs, and haft-rang underglaze ceramic tiles related to the cuerda seca method. Tiles were favored on exteriors for their resistance to weathering.
Gawhar Shad, who died in 1457, was the wife of Shah Rukh and one of the most important architectural patrons of the 15th century. She commissioned the Goharshad Mosque in Mashhad between 1416 and 1418 and built a mausoleum and mosque complex in Herat between 1417 and 1438. Her chief architect was Qavam al-Din al-Shirazi.
The Bibi Khanum Mosque in Samarkand was built between 1399 and 1405 and was among the largest mosques in the world at the time of its completion. It was named after Timur's wife, whose mausoleum stands across from it. The mosque features an imposing portal, a large courtyard with four iwans, and four minarets along its front facade.
Earlier Iranian domes rested on an octagonal base formed by four squinches transitioning from a square chamber. Timurid domes instead sat on arches built over the edges of the square chamber, with concave spandrels filling the gaps to form a more circular base, making the vertical transition between chamber and dome far more dynamic.
The Timurid style spread to the Ottoman Empire in the west, the Mughal Empire on the Indian subcontinent (whose rulers were descended from Timur), and the Safavid Empire in Iran. Even the Qara Qoyunlu and Aq Qoyunlu confederations in western Iran showed Timurid influence while the empire was still standing.