What is the decisive Quranic and Prophetic cure for obsessive-compulsive disorder (OCD) that causes doubt concerning the existence of Allah, Paradise, and Hell, and is such doubt considered a departure from the religion?

Waswasa (whispering from Satan) is an affliction from Satan, and its cure lies in completely ignoring it, and in frequently remembering Allah, reciting the Quran, and performing adhkar (supplications). Your crying out of fear of disbelief is a good sign, and one who is like that cannot be a disbeliever. As for your feeling of showing off (riya') in good deeds, that is also from Satan's trickery to discourage you. Its cure is to continue performing good deeds and to anger Satan. Be keen on attending gatherings of goodness and associating with righteous women to work on spreading da'wah (inviting to Islam), enjoining good, and forbidding evil, so that Allah's mercy may encompass you.