1. The Khawaarij are a group who first appeared in the time of Alee (radiallaahu anhu). They split from his army and began the grave innovation of Takfeer (declaring Muslims, rulers or the ruled, in their view guilty of major sins, to be disbelievers). The Prophet warned against them in many authentic ahaadeeth: The Khawaarij are the dogs of the Fire. Reported by Ahmad and it is saheeh. He also informed us that they would continue to appear until the end of this world, saying, A group will appear reciting the Quraan, but it will not pass beyond their throats. Every time a group appears, it is to be cut off, until the Dajjaal appears within them. Reported by Ibn Maajah and it is hasan. Refer to Silsilatul-Ahaadeeth as-Saheehah (no.2455).
2. Refer to the hadeeth reported by Ibn Abbaas (radiallaahu anhumaa) mentioned in the footnote to point number two of the book.