Short answers, pulled from the story.
An onion dome is a specific type of roof that resembles the bulbous form of an onion. This geometry distinguishes them from other Eastern Orthodox cupolas like helmet domes found on the Dormition Cathedral in Vladimir.
Historian Wolfgang Born traces the origin of this architectural feature to Syria. Umayyad Caliphate-era mosaics depict early stages of the development of bulbous domes there.
Buildings featuring onion domes appeared in Russia as early as the 13th century. The domes of Saint Basil's Cathedral have not been altered since the reign of his son Fyodor I, indicating their presence in sixteenth-century Russia.
The first one was built in 1576 by the architect Johannes Holl on the church of the Convent of the Franciscan Sisters of Maria Stern in Augsburg. Usually made of copper sheet, these domes appear on Catholic churches all over southern Germany.
The onion dome is used extensively in Mughal architecture which later influenced Indo-Saracenic architecture. It is also a common feature in Sikh architecture particularly within Gurudwaras and appears in numerous mosques in Indonesia.