Short answers, pulled from the story.
The Arabic root word salata means to be hard or strong. This verbal noun evolved into the abstract concept of sul tan, which initially designated moral authority rather than political power.
Towards the late 10th century, the term began denoting an individual ruler with practically sovereign authority. The first major figure to clearly grant himself this title was Mahmud of Ghazni who ruled from 998 to 1030 CE over present-day Afghanistan and surrounding regions.
This event eliminated remnants of Abbasid political power and surviving descendants lived in Cairo under Mamluk protection while effectively having no authority. The Mamluks recognized themselves as sultans while protecting the line of the Abbasid caliphs and argued that only they could hold that title.
Brunei Malaysia and Oman remain the only sovereign states retaining the title sultan for their monarchs. Morocco changed its style from sultan to king on the 14th of August 1957 under Mohammed V.
A feminine form of sultan is sultana or sultanah used by Westerners for some Muslim women monarchs. Turkish and Ottoman Turkish also uses sultan for imperial ladies since grammar uses same words for both genders.