First, based on Rizvi (1987) Chapter VI:
1. Abul-Fazl Gaziruni )d.1602)- author of Akbar-nama, in two parts.
2. [Reminds me of historical writings by Islamic authors for South Asia, Tarikh-i Firishta, written by Muhammad Qasim Hindu Shah Astarabadi]
3. Abul-Fazl's brother is the poet-laureate of Akbar's court, whose Persian poetry is influential in Safavid Iran.
4. Key Sufi orders ("silsilas"):
> Suhrawardiyya: Indian founder Ahaykh Bahaud-Din Zakariyya ~1182-3)
> Chishtiyya: sounds like the most important silsila; essentially an Indian order; founded in Indian by Khwaja Muinud-Din (d. 1236); key saints include Baba Farid (d. 1265), whose successor was Shaykh Nizamud-Din Awilya (d. 1325), whose successor in Delhi was Shaykh Nasirud-Din Mahmud (a.k.a. "Chiragh of Delhi"), whose theachings are embodied in the Khayrul-majalis, compiled by one of his disciples - said to represent a peak in Chishtiyya philosophy
> Shattariyya: founded by Shah Abdullah (d.1485); Ghaws Shattari (d. 1563) has a famous work called Jawahir-i khamsa.
> Qadiryya: important figure was Shaykh Abdul-Haqq Muhaddis Dihlawi (d. 1642) - fame rest on his works of hadis named "Madarijun-Nubuwwah". He supports moderate, reconciling views. Dara Shukoh, Shahjahan's eldest son was in this order and wrote sufi treatises, including Majmaul-bahrayn ("The Mingling of Two Oceans"), and translated (with help) of Upanisads into Persian
> Naqhbandiyya: famous figure Shykh Ahmad Sirhindi (d. 1624), styled himself Mujaddid ("the renewer"), holds Wahdat-al-Shuhud view against the more prevalent (Ibn Arabi's)Wahdat al-Wujud view.
[5. Overall, my impression is these Sufi orders rely very heavily on genealogies (who is teacher of whom), often juggle for court's favor (most obvious around Akbar's successors' times).]
6. al-Biruni's Kitab fi tahqiq ma lil-Hind.
7. Sayyid Muhammad (d. 1505)- founder of Mahdawi movement
8. Shii: most learned in Akbar's reign was Qazi Nurullah Shustari
9. Shah Waliullah - whose analysis of history of Sufism Rizvi quotes. He is also the only Indian Islamic figure with his own chapter in History of Islamic Philosophy (edited by Sayyed Hossein Nasr)
Second, based on Basham (1984), two chapters (19, 33) written by the same Rizvi:
1. Shaykh Nasirud-Din Mahmud's nephew's Chandain writtin in 1379-80 was considered Hindawi poetry having reached a higly developed stage
2. Qazi Nurullah Shustari has a famous book ("Pious Banquet") on Shii history that includes all famous Sufis as Shiites
3. Prince Dara Shukoh translated 52 Upanisads into Persians in in 6 months of 1656-1657 with Hindu Sanskritist.
4. Indian Islamic scholars (e.g. in hadith) has works recognized classics by wider Islamic circles; some Shattariyyas have hadith students in Mecca / Medina from Malay.
5. Amir Khusrow (1253-1325): most important work is ghazals, recognized as great works by Persian poets. "Indian style" actually dominated Persian poetry in 16th-17th century.
Based on Hodgson's The Venture of Islam Vol 2, Amir Khusrow is of the Chisti order, known for his ghazals and epics, and was Nizamuddin Awliya's disciple.
I've read more today from Hodgson (notes to be written later, too late already), and am planning to read the chapters in Nasr's History of Islamic Philosophy.