Short answers, pulled from the story.
Construction of the stone cathedral began in 1555 to replace wooden memorial churches. The building received its final colors and tiled cornice in 1683 after a major expansion phase between 1680 and 1683.
The identity of the architect remains unknown to historians despite tradition naming Barma and Postnik Yakovlev as builders. Some researchers suggest these names refer to the same person, either Postnik Yakovlev or Ivan Yakovlevich Barma.
Contemporary records identify the building as Trinity Church after its easternmost sanctuary. The status of kathedron or large assembly church had not yet been bestowed upon it at the time of completion.
Many historians believe the story is false because Postnik Yakovlev remained active throughout the 1560s. He participated in constructing the Cathedral of the Annunciation in Moscow alongside building walls and towers of the Kazan Kremlin.
In 1923 the building became a public museum though religious services continued until 1929. Bolshevik planners entertained ideas of demolishing the church after Lenin's funeral in January 1924 but eventually spared it by 1937.