Short answers, pulled from the story.
Mulla Sadra, fully Sadr ad-Din Muhammad Shirazi, was an Iranian Twelver Shi'i Islamic mystic, philosopher, theologian, and 'Alim who lived around 1571/2 to 1635/40 CE. According to Oliver Leaman, he is arguably the single most important and influential philosopher in the Muslim world in the last four hundred years.
Transcendent Theosophy, or al-hikmah al-muta'aliyah, is the school of philosophy Mulla Sadra founded by synthesizing the Islamic Golden Age philosophies. It combined Avicennism, Suhrawardi's Illuminationist philosophy, Ibn Arabi's Sufi metaphysics, and Sunni Ash'ari Kalam theology within the framework of Twelver Shi'ism.
Mulla Sadra held that existence precedes essence and is principal, since something must exist first and then have an essence. For him this was a question of cosmology tied to God's position in the universe, and his metaphysics gives priority to existence over essence, treating essences as variable while immutability belongs to God alone.
Substantial motion, al-harakat al-jawhariyyah, is Mulla Sadra's theory that everything in nature, including the celestial spheres, undergoes substantial change and transformation. Unlike Aristotle and Avicenna, who accepted change in only four categories of quantity, quality, position, and place, Sadra extended change to the category of substance itself.
Mulla Sadra moved to Qazvin in 1591 and to Isfahan in 1597 to study philosophy, theology, Hadith, and hermeneutics in Safavid capitals. His teachers were Baha' ad-Din al-'Amili and Mir Damad, and he always introduced Mir Damad as his true teacher and spiritual guide.
Mulla Sadra died around 1635 to 1640 CE in Basra after performing the Hajj. He was buried in the present-day city of Najaf, Iraq.
Mulla Sadra's main work is the Hikmat al-Muta'alyah fi-l-asfar al-'aqliyya al-arba'a, known as the Transcendent Philosophy of the Four Journeys of the Intellect, or simply the Four Journeys. He began it around 1015 AH (1605 AD) and took almost 25 years to complete it, finishing some years after 1040 AH (1630 AD), in four large volumes.