What is the ruling on one who delays joining the Imam in bowing (rukūʿ) or prostrating (sujūd) in order to complete Al-Fatiḥah or to firmly place his forehead on the ground?

Your prayer is valid in both scenarios you mentioned, according to the majority of scholars, and you are not required to repeat it. We caution you against obsessive thoughts (waswas) and urge you to strive against them and work towards getting rid of them.