Short answers, pulled from the story.
Vaishnavism originated during the 7th to 4th century BCE as a fusion of various regional non-Vedic religions with worship of Vishnu. Scholars suggest it formed from popular theistic traditions like the Bhagavata cults before being identified with the Vedic God Vishnu in early centuries CE.
Heliodoros was an envoy from the Greco-Bactrian king Amtalikita who declared himself a bhagavata devoted to Vasudeva on a pillar carved into stone in 115 BCE. This artifact represents one of the earliest unambiguous images of the deity found by numismatic and sculptural evidence at modern Vidisha in Madhya Pradesh.
The four major theological denominations are the Vishishtadvaita school founded by Ramanuja, the Dvaita school founded by Madhvacharya, the Dvaitadvaita school founded by Nimbarkacharya, and the Shuddhadvaita founded by Vallabhacharya. These schools emerged between the 12th and 13th centuries CE to challenge Advaita Vedanta interpretations.
The Alvars appeared between the 5th century to the 10th century CE as twelve Tamil poet-saints who espoused bhakti devotion to Vishnu or Krishna. Their devotional writings known as the Naalayira Divya Prabandha were key texts that helped establish the Bhakti movement which spread from South India northwards during the 7th-century CE.
A. C. Bhaktivedanta Swami Prabhupada founded the International Society for Krishna Consciousness ISKCON in 1966 to spread Gaudiya Vaishnavism to the West. This movement has grown to become the largest Hindu sect with an estimated 399 million adherents according to a 2020 estimate by The World Religion Database.