Short answers, pulled from the story.
Mir Damad founded the School of Isfahan. He was the nephew of Muhaqiq Karaki, an influential Shia scholar, and Henry Corbin described him as possessing an analytic mind with a strong awareness of the religious foundations of knowledge.
The name School of Isfahan was coined by Seyyed Hossein Nasr and Henry Corbin. They identified and named the school retroactively, recognising the coherent philosophical tradition that had formed in Isfahan during the Safavid era.
Mulla Sadra brought the School of Isfahan to its fullest development. He studied under three of the school's masters, including Shaykh-i Baha'i and Mir Damad, though he developed significant philosophical disagreements with Mir Damad over theories of time.
The School of Isfahan drew on Avicennism, Averroism, and the illuminationist tradition of Suhrawardi, as well as the earlier Shiraz school of philosophy. Figures such as Ibn Turkah, Qadi Maybudi, and Ibn Abi Jomhour Ahsaei also played foundational roles.
The Safavid court under Shah Abbas provided funding for the arts and intellectual life, making Isfahan a famous academic city and Iran's intellectual centre. The court also backed the declaration of Shia Islam as the formal religion of Persia, shaping the school's religious and philosophical priorities.
Shaykh-i Baha'i was one of the three masters of Mulla Sadra and served as chief jurist on the Safavid Court. He coined the term Hikmat-e Yamani, meaning the wisdom of believing, and argued in his philosophy that humans are the only being capable of intelligence.