Can God forgive someone who has committed sodomy if he repents, and can he live a normal life thereafter?

Allah has promised those who repent that He will accept their repentance and forgive their sins, as stated in His Almightyقوله تعالى: "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.""

For repentance from immoral acts, the following is recommended: 1. Increase in good deeds: For good deeds erase evil ones. 2. Associate with the righteous: And distance oneself from evil people, as a person is influenced by those he accompanies. 3. Close off pathways leading to immorality: This includes lowering one's gaze from effeminate men and avoiding seclusion with them. 4. Expedite marriage if possible: Otherwise, fast, for it is a shield.

As for the Hadd punishment, it is the prerogative of the ruler and it is not permissible for an individual to inflict it upon themselves.