Are Ibn Hazm, Al-'Izz ibn 'Abd al-Salam, and Abu Hanifa considered among the People of the Sunnah?

Abo Hanifa is one of the four Imams, and his madhhab (definition) is the oldest of the madhhabs. Sheikh Al-Izz ibn Abd al-Salam is an Imam among the Imams of Ahl al-Sunnah (definition), nicknamed "Sultan al-Ulama" (Sultan of Scholars) due to his strength in denouncing evil. He was expelled from Damascus for condemning the Sultan's surrender of Muslim lands to the Franks. Ibn Kathir described him as the Sheikh of the Shafi'i madhhab in his time, and he has excellent works. As for Ibn Hazm al-Zahiri, he was a brilliant and حافظ (memorizer of hadith (definition)) scholar who excelled in the Shariah sciences and authored many books. However, he was a Zahiri in subsidiary matters, not accepting qiyas (definition) (analogical reasoning), which is what positioned him among the scholars. He was also one of the most ardent in figurative interpretation (ta'wil) in the chapter of Usul (fundamentals of religion) and the attributes of Allah, due to his profound knowledge of logic.