What should I do concerning the prayers I previously performed without completing the bowing (rukūʿ) or uttering "Rabbana wa laka al-hamd" (Our Lord, to You be all praise) or "Allahu Akbar" (God is the Greatest) after bowing, given that I was unaware of the religious ruling at the time, and I do not know the number of these missed prayers?

There are two different matters in prayer: omitting a pillar (rukn) and omitting an obligation (wajib (definition)). Whoever omits a pillar must return to perform it, such as someone who forgets the bowing (ruku') then remembers it while prostrating (sajid). In this case, he must stand up to perform the bowing. If he remembers it after reaching the bowing of the next rak'ah, the next rak'ah is considered to have taken the place of the previous one, and he must perform another rak'ah to replace the one whose pillar he omitted. As for obligations, such as saying "Our Lord, and to You be praise" (Rabbana wa laka al-hamd) or the takbir (Allahu Akbar), one does not return to them if they were omitted due to forgetfulness. Instead, they are compensated for by the prostration of forgetfulness (sujud (definition) al-sahw).