An Abbassid is a member of the dynasty of caliphs which ruled from Baghdad from around 750 to 1250, claiming ancestry of Abbas.
The Abbassid Caliphate was responsible for setting up vast trade routes. Abbassid coins have been found in China and Sweden, which shows just how vast these routes were. This created a cosmopolitan economy in Baghdad, the Abbassid Capital.
The Abbassids built Baghdad, in modern-day Iraq, as their capital. It remained their capital until Hulegu Khan sacked it and destroyed the Abbassid Caliphate.
The Abbassid Caliphate capital was moved to BAGHDAD, IRAQ, because Syria had an Umayyad power-base and Baghdad was much closer to Persia, which was the Abbassid power-base.
Abbas ibn Abd al-Muttalib established the Abbassid Dynasty.
Yes they were! Most famously, the Mamluk Core of the Abbassid Army (comprising the majority of the Abbassid military divisions) was made entirely of enslaved Turkish people. Eventually the Mamluks turned on the Abbassids and established their own empires.
The Abbassids were ruled by Kings who styled themselves Caliphs (since all previous rulers of the Moslem Empires had done similarly. The First Abbassid Caliph is Abu Al-Abbas As-Saffah. He ruled from 750 CE to 754 CE and was succeeded by the Abbassid Al-Mansur (there is a different Umayyad Al-Mansur in Spain in the 900s).
Abbas ibn Abd al-Muttalib established the Abbassid Dynasty.
Hülegü Khan of the Mongols conquered Baghdad in 1258, effectively ending the Abbassid Caliphate.
The Seljuk Turks (Sunni Muslims) conquered the city form the Abbassid Arabs (Sunni Muslims).
Hülegü Khan, a grandson of Genghis Khan by his son Tolui, who led the conquest of the Persian and Abbassid Caliphates, destroying numerous cities and gaining a place of infamy among Middle Easterners. He founded the Ilkhanate, the Mongol Empire that ruled Persia, Mesopotamia, and eastern Anatolia for 1256-1335.
The Islamic Golden Age occurred primarily under the auspices of the Abbassid Empire.
Al-Khwarizmi was not forced to do math; he did it out of interest and ability. However, the government under which he worked was the Abbassid Caliphate.