Short answers, pulled from the story.
Vajrayana Buddhism emerged as a distinct movement during the 5th century and developed into separate tantric traditions by the 7th century. This spiritual current arose from pre-existing Tantric traditions within Hinduism that had been developing during the first millennium CE.
Mahasiddhas were wandering yogis who thrived during the latter half of the first millennium and practiced methods radically different from traditional monasteries. They engaged in practices on charnel grounds and sometimes included taboo substances, with at least two comparable to Shaiva Nath saints such as Gorakshanath and Matsyendranath.
The philosophical view of Vajrayana is based on Mahayana Buddhist philosophy, mainly the Madhyamaka and Yogacara schools. It emphasizes the theory of emptiness and uses negative mental factors like desire and hatred as part of the path toward liberation.
Vajrayana teachings have been passed down through an unbroken lineage going back to the historical Buddha via other Buddhas or bodhisattvas like Vajrapani. The tradition spread rapidly across Southeast, East, and Central Asia, giving rise to unique schools in Tibet and Japan by the 7th century.
Padmasambhava was invited by King Trisong Detsen sometime before the 2nd of May 767 along with Śāntarakshita. This event marked a significant point in the development of Tibetan Buddhism which became the dominant spiritual tradition integrating local beliefs and practices.