Is my feeling of hypocrisy (riyaa') during ablution (wudu') and prayer, and my repetition of them because of that, valid, or is repetition not obligatory even if my soul tells me so, knowing that I seek refuge in Allah from Satan and recite the prescribed supplication?

The Muslim must intend by his work the Face of Allah Almighty alone, and beware of showing off (riya') which invalidates the deed and may lead to polytheism (shirk (definition)); for Allah accepts only the deed that is sincerely for His Face and is in accordance with the Sunnah (definition) of His Prophet Muhammad, peace and blessings be upon him, as stated in the Hadith (definition): "I am the most independent of partners from partnership. Whoever does a deed in which he associates another with Me, I abandon him and his shirk."

However, the Muslim must also not open a door for Satan to cast doubt on his intention, which might lead him to abandon the good deed under the pretext of lacking sincerity. This is a satanic whisper that one must guard against. Rather, the obligation is to sincerely dedicate one's intention to Allah and fight against the self turning to anyone else, and not pay attention to whispers thereafter. Thus, one should not repeat purification or prayer.