Here are the answers to your questions:
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Who led the Abbasid rebellion against the Umayyad dynasty?
Answer: Abu al-Abbas al-Saffah -
Where was the caliphate moved to after the Abbasids took control?
Answer: Baghdad -
Who wrote the book "Kitab al-Jabr wa-l-Muqabala"?
Answer: Muhammad ibn Musa al-Khwarizmi -
What was one of the key features of the Islamic Renaissance?
Answer: A climate of intellectual and cultural exchange. -
What factors contributed to the decline of the Islamic Renaissance?
Answer: Political and social instability, and the rise of more conservative religious movements.