What was the political state of the middle east following the fall of the Abbasid empire and the fall of the Mongols?

Answer 1

The two empires did not fall simultaneously. The reason the Abbassid Caliphate fell in the Middle East was because the Mongol Empire defeated it and installed the Ikhanate. As a result, the political state of the Middle East following the fall of the Abbassids was the Ikhanate in most areas, the Mamluks in the Levant and Egypt, and the untouched Arabian Emirates (like the Sharifate of Mecca, the Emirates of the modern UAE, Oman, etc.)

The fall of the Ikhanate in 1341 led to the development of many smaller piecemeal kingdoms throughout the former territories of the Ikhanate. The smaller states in Persia were conquered relatively quickly by the Timurids of Transoxiana. Elsewhere in the Middle East, these smaller states would later be conquered by the Ottoman Empire. The Mamluks held their position in the Levant until the Ottomans eventually conquered them as well. The Arabian Emirates remained untouched.