Does committing sins in private nullify the reward for previous good deeds, and if the sinner repents sincerely after performing good deeds and committing sins in private, does he retain the reward for his past righteous acts?

The hadith (definition) you referred to is an authentic hadith and contains a severe warning for those who fear people and consider Allah to be the least significant of those watching them. However, the texts of the Qur’an and Sunnah (definition) do not pertain only to sinners; rather, they encourage the sinner to repent and clarify that one who repents sincerely is like one who has no sin, and that Allah replaces their evil deeds with good ones. There are also adhkar (remembrances) and actions in the Sunnah that expiate sins. Thus, the Book and the Sunnah contain both warnings and encouragement, and the believer worships through both, balancing between fear and hope. Ahl al-Sunnah wal-Jama’ah (the People of the Sunnah and the Community) deal with all the texts of revelation; they do not limit themselves to the texts of warning and despair, nor to the texts of promise and thus commit evil deeds. We advise you to improve your actions to please Allah and to have a good opinion of Him, while not feeling secure from Allah’s plan, and to seek beneficial Islamic knowledge.