Short answers, pulled from the story.
Emperor Nicholas I lifted the state monopoly on architectural styles in 1832. This decision ended decades of enforced Empire style and allowed architects like Konstantin Thon to create eclectic church designs.
Roman Kuzmin designed the Church of Dmitry Solunsky between 1861 and 1866. The structure features a flattened main dome blended into a cylindrical arcade resting on a cubical structure with four apses instead of two.
Emperor Alexander II reigned from 1855 to 1881 during which time Neo-Byzantine architecture became the officially endorsed preferred style for church construction. Prince Grigory Gagarin served as the most influential supporter through published studies of Caucasian and Greek heritage alongside service to empress Maria Alexandrovna.
Exposed masonry replaced flush stucco surfaces required by Neoclassical canons while wide bands of dark red base brickwork interleaved with narrow stripes of yellow or grey brick set slightly back into walls became standard decoration. Hemispherical domes crowned every Byzantine church often featuring a small curvilinear pointed top at the base of a cross otherwise mounted directly at the flattened apex.
By 1894 there were 47,419 temples including 695 major cathedrals though most belonged to late 19th century variants of Russian Revival instead. Nearly all of the 5,000 churches attributed to Alexander III were financed through public donations while state funding remained reserved for palace churches catering directly to royalty.