Can a disobedient person who has associated partners with God repent and be accepted by God into His mercy, and will God forgive him for this sin, or must the Hadd punishment for apostasy be carried out against him?

If you repent with sincere repentance and regret your sin, then Allah the Almighty accepts your repentance and forgives your transgression, in affirmation of His saying, exalted be He: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" and His saying, exalted be He: "Except for those who repent, believe and do righteous deeds; for those, Allah will change their evil deeds into good ones. And Allah is Forgiving and Merciful." The verse that speaks of not forgiving shirk (definition) (associating partners with Allah) applies to those who do not repent. Whoever repents to Allah the Almighty, Allah turns to him in forgiveness. So rejoice in Allah's acceptance of your repentance, persevere in fulfilling your obligatory duties, and abandon what Allah has forbidden, for good deeds erase evil deeds.