Islam's role:
The Delhi Sultanate itself was established by Muslims and hence Islam played a major role in the Royal Court. For the next 6 centuries almost all rulers of Delhi Sultanate and the Maugham Empire were Muslims.
This, and the close connections of the rulers with Central Asia meant that they brought those languages and Arts with them.
Hinduism's role:
The Muslim rulers conquered a land that was predominately Hindu and they took the time and effort to understand the subject. Many of the concubines and governors were Hindu and the kinds even learned from the language. One Mughal King even tried to create a new religion that combined Islam and Hinduism.
Christianity Role:
Christianity was not even a minor religion during the Delhi Sultanate. Small missionary groups from Europe did visit and most Kings were tolerant of them.
The Umayyads were the first Muslim dynasty to achieve success after caliph rule.
