Short answers, pulled from the story.
Brick served as the primary building material throughout this era. Large surfaces of brick were covered using banna'i tiling techniques to create geometric patterns and Kufic inscriptions at relatively low cost.
The Mausoleum of Khoja Ahmed Yasawi stands in Turkestan, present-day Kazakhstan, built between 1389 and 1399. This massive funerary complex surrounds the tomb of a local Sufi saint named Ahmad Yasawi.
Gawhar Shad became one of the most significant architectural patrons during the first half of the 15th century until her death in 1457. Her mausoleum and mosque complex in Herat were built between 1417 and 1438 before being partially demolished by British forces in 1885.
Timurid architects placed arches over square chamber edges instead relying on squinches only at corners. Concave spandrels filled small spaces between arch tops forming circular bases for upper domes to create dynamic vertical transitions between chambers and domes.
To the east it transmitted to the Indian subcontinent through Mughal descendants of Timur while Safavid rulers in Iran inherited the Timurid style developing their own imperial architecture further. The international Timurid style eventually integrated into visual culture of the rising Ottoman Empire in western regions.