Short answers, pulled from the story.
Scholars coined the label Old Hindi centuries after the language itself fell silent to describe the ancestor of Modern Standard Hindi. The word Hindi literally means Indian in Classical Persian and was also called Hindustani during the Delhi Sultanate.
Delhavi Khariboli flowed through the region around Delhi between the 12th and 14th centuries while speakers lived under the rule of the Delhi Sultanate. This specific dialect served as daily communication for people in the capital region during these three hundred years.
Muslim rulers introduced Persian vocabulary into the existing Prakritic base of the language which transformed the original structure into early Hindustani. These loanwords accumulated within speech patterns to create a hybrid tongue capable of serving both Hindu and Muslim communities.
Amir Khusrau wrote verses that document the language in use during his lifetime as an Indo-Persian Muslim poet whose works survive as key evidence. Namdev composed verses as a Vaishnava Hindu poet that also reflect the dialect while Baba Farid contributed some verses found in the Adi Granth text.
Hindi languages were originally written in different variants of Nagari writing systems before scribes later adopted the Arabic script using Nastaliq calligraphy techniques. The shift from Nagari to Nastaliq allowed the spoken dialect to be recorded by Muslim scribes based on religious tradition and political context.
The majority view places the starting point several centuries later between the 12th and 14th centuries rather than the earlier Apabhraśa poetry dated 769 AD. R.A. Dwivedi saw the earliest period of Hindi literature extending from 760 AD up to the eleventh century but such an early date has not been generally accepted by most experts.