Is my prayer valid, taking into account all the mentioned pillars, duties, and recommended acts, without distinguishing between them, and with the repetition of the letter 'R' in Al-Fatiha and other surahs? And is it permissible for me to pray according to the Hanbali school of thought, and what is their ruling on this issue?

Your prayer is valid, and there is no harm in you acting upon the opinion of the Shafi'is that repeating the letter 'ra' does not invalidate it. Taking the easier opinion is a way to remove hardship. Your ignorance of whether some actions are sunnah or fard does not invalidate it. The advice for those afflicted with waswas (obsessive whispering) is to turn away from it and ignore it, for indulging in it leads to great evil.