What is the legitimacy of the Umayyad Caliphate, and is Al-Hajjaj ibn Yusuf Al-Thaqafi among the people of Paradise or Hell, and is the caliphate of Abdullah ibn Al-Zubayr valid, and what is the status of the Khawarij?

Al-Hajjaj ibn Yusuf Al-Thaqafi was not a Caliph but rather a governor of Iraq and the East for Abd al-Malik ibn Marwan. Al-Dhahabi described him as unjust, tyrannical, and a Nasibi (one who harbors hatred for Ali and his family), indicating that his good deeds were submerged in a sea of his sins. However, he did not commit disbelief (kufr), and his judgment is with Allah. As for Abdullah ibn Al-Zubayr, he was a venerable Companion and the son of the Apostle of Allah's (peace be upon him) disciple (hawari). Ibn Abbas and Al-Dhahabi praised him. He was pledged allegiance as Caliph after the death of Yazid and ruled vast regions before being killed by Al-Hajjaj. Ibn Al-Zubayr was diligent in accepting the caliphate and rejecting its inheritance. His status necessitates invoking Allah's pleasure upon him and refraining from delving into the mistakes of the Companions, for the Prophet (peace be upon him) said: "Do not revile my Companions." The caliphate of the Umayyads was considered valid by scholars, as was the imamate of the one who gained power by force. The Khawarij rebelled against Ali ibn Abi Talib but were not deemed disbelievers.