Is the repentance of someone who intentionally committed a sin—despite it being the result of obsessive-compulsive disorder—accepted, and will God forgive him? Is he permitted to marry a Muslim woman while in this state, and would his wife be lawful for him?

This question stems from a whisper (waswasa) that should be completely disregarded. You should consult doctors, strive in supplication (du'a), and perform lawful incantations (ruqya shar'iyya). Repentance is accepted from everyone, no matter how great their sin. Allah the Almighty says: "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.'" Your marriage is valid, your living with your wife is lawful, and you are a Muslim. Do not surrender to the whispers of Satan.