What is the ruling on psychological and creedal turmoil, and doubting the existence of God and the Hereafter, despite adherence to worship and good deeds?

If bad thoughts are merely whisperings (waswasah) and self-talk (hadith al-nafs), and the heart does not assent to them, then they will not harm you. You must turn away from them and strive to repel them, and you will be rewarded for that. Frequently seek refuge with Allah from Satan and say "I believe in Allah" when these whisperings occur. Continue with good deeds.