Is the prostration of forgetfulness (sujūd al-sahw) required when repeating or re-saying a word in Al-Fatiha due to doubt, or repeating a word in a verbal Sunnah, and is it permissible to adopt the dispensations (rukhsa) in prayer when experiencing frequent obsessive doubts (waswasa)?

You should continue to strive against the whispers (waswas) and get rid of them. Therefore, do not repeat the recitation of Al-Fatiha or the Tashahhud if you doubt them. You are not required to perform the prostration of forgetfulness (sujud al-sahw), whether you disregard the whispers or repeat some words because of them. There is no harm in adopting credible opinions that make it easier for you and help you recover from the waswas.