なさるTo do (Honorific)

Both なさる and する express performing an action, similar to the English 'do.' The key difference is politeness: する is the standard, neutral term used in everyday contexts, while なさる is an honorific expression used to 'elevate' someone else's actions with respect to you (or your in-group).

いたす is the humble form of する, used when talking about your own actions to someone respected. For example, 連絡いたします means 'I'll contact you.' in a deferential way. なさる is the opposite: the honorific form used when referring to the respected person's actions, as in ゴルフをなさいます ('He/she plays golf.').

なさる and なさい are derived from the same verb but used differently. なさる is an honorific form of する, used for respectful reference to someone's actions, as in 明日仕事なさいますか？ ('Will you be working tomorrow?'). なさい is the imperative form, used to firmly but politely instruct someone, as in 宿題をしなさい ('Do your homework.').

Both are honorific forms. お～になる is used for regular verbs, like 答える 'answer' becoming お答えになる (same meaning, but showing respect to the answerer). なさる is the specific honorific form of する, e.g. ゴルフをなさる means '(He/she) plays golf.' in an honorific/respectful sense. Since する is irregular, it does not use the お～になる pattern.