Was Harqus ibn Zuhayr al-Sa'di a Kharijite or a hypocrite, and do hypocrites engage in jihad?

It is not possible to definitively ascertain the identity of Harqus ibn Zuhayr al-Sa'di due to the absence of reliable narrations that decisively establish his circumstances. It has not been proven that he is Dhu al-Khuwaysirah al-Tamimi, who reproached the Prophet, peace and blessings be upon him. Dhu al-Khuwaysirah al-Tamimi is distinct from Dhu al-Thudayyah the Kharijite, and it has not been definitively established that his name was Harqus; rather, the narrations that mentioned his name are weak or contain objectionable elements. Furthermore, no authentic narration has been proven that names Dhu al-Thudayyah the Kharijite as Harqus. The reports that mentioned Harqus ibn Zuhayr's participation in the conquests and then his joining the Kharijites came with weak and abandoned chains of transmission that are not to be relied upon. In summary, nothing reliable has been proven regarding Harqus ibn Zuhayr.