Does mispronouncing the letter “raa” or repeating it, especially during the Takbir, affect the validity of the prayer? And is it permissible to suffice with reciting Al-Fatiha once, despite the errors, to avoid Waswasa (obsessive doubts) and re-offering the prayer?

Repeating the letter 'R' (راء) in the Takbir does not invalidate the prayer. If you experience obsessive thoughts (waswasah) regarding the articulation points of letters or their repetition in the Takbir or Al-Fatiha, disregard them, as they are from Satan, and do not repeat the prayer. Scholars have stipulated that if obsessive thoughts concerning the articulation points of letters, their emphasis, or doubt about reciting Al-Fatiha and similar matters become frequent, one must ignore them.