Short answers, pulled from the story.
A queen consort is the wife of a reigning king and does not hold independent ruling power. A queen regnant is a female monarch who rules in her own right, usually by inheriting the throne.
A queen dowager is a widowed queen consort. A queen mother is a queen dowager who is also the mother of the current reigning monarch.
Haseki sultan was the title held by the lawful wife and imperial consort of the Ottoman sultan. It was first used in the 16th century by Hurrem Sultan, wife of Suleiman the Magnificent, replacing the earlier informal title of Bas Kadin, meaning Head Lady.
The title of king historically ranks higher than queen, so giving a queen's husband that title would place him above her in the hierarchy. Prince consort identifies his status without outranking the sovereign. Prince Albert of Saxe-Coburg and Gotha received this title when he married Queen Victoria, at her insistence.
Yes. When a monarch died and left a minor heir, the widowed queen consort often became regent. Examples include Marie de' Medici for Louis XIII of France, Queen Regent Anne for Louis XIV of France, and Queen Emma of Waldeck and Pyrmont, who served as regent for her daughter Wilhelmina from 1890 to 1898 after William III of the Netherlands died on the 23rd of November 1890.
Queen Charlotte, consort of George III, was Britain's longest-tenured queen consort. She held the position for 57 years and 70 days, from 1761 to 1818.