Is a marriage considered valid if it was contracted while a person doubted their religion and faith, and was overwhelmed by distress and fear at the time of the contract?

The marriage is valid, and there is no doubt about its validity. As for doubting the Book of Allah, it is among the whispers (waswas) that do not cause harm if the person dislikes them; rather, it is pure faith. It is narrated from Abu Hurayrah that he said: A man came to the Messenger of Allah, peace and blessings be upon him, and said: O Messenger of Allah, I find in myself thoughts that I would rather fall from the sky than utter them. He (the Prophet) said: "That is pure faith."

To overcome these whispers: Increase prayer, remembrance of Allah (dhikr), and supplication (du'a). Turn away from the whispers and do not dwell on them. Engage in learning matters of religion.