Short answers, pulled from the story.
Old Hindi emerged during the 12th to 14th centuries within the bustling markets and courtyards of Delhi while the Delhi Sultanate reshaped northern India. This period marks the time when the spoken vernacular known as Khariboli or Delhavi began to develop its distinct identity separate from its Prakritic and Apabhraśa predecessors.
The Indo-Persian Muslim poet Amir Khusrau composed verses that stand as some of the earliest attested examples of the language. The Vaishnava Hindu poet Namdev, the Sufi Muslim Baba Farid, and the Bhakti Hindu poet Kabir also contributed to this literary tradition using the same dialect.
Hindi languages were originally written in various variants of the Nagari script which had evolved from ancient Brahmi. As the language came under the influence of Persian culture, it began to be written in the Arabic script specifically in the elegant Nastaliq calligraphy style favored by Muslim poets and courtiers.
A minority of scholars include Apabhraśa poetry as early as 769 AD citing the Dohakosh by Siddha Sarahapad as evidence of an early Hindi literary tradition. This early dating is not generally accepted by the broader academic community as it requires subsuming a large body of Apabhraśa literature into the Hindi category which many find linguistically problematic.
The transformation of Old Hindi into Hindustani was a gradual process driven by centuries of cultural interaction and political change. As Persian loanwords were absorbed into the Prakritic base of Old Hindi the language began to evolve into a new form that would eventually become the standard for both Hindi and Urdu.