Is it necessary for raising the hands to be after standing up straight from bowing (rukūʿ), or during the process of rising from it? And is the saying "Samʿa Allāhu liman ḥamidah" (Allah hears those who praise Him) obligatory for the one being led in prayer (maʾmūm)?

It is Sunnah (definition) to raise the hands to the level of the shoulders when pronouncing the takbir for bowing (ruku') and when rising from it, but this raising is not obligatory. The hands should be raised either simultaneously with lifting the head or after straightening up. The congregant (ma'mum) should say "Our Lord, and to You be praise" (Rabbana wa laka al-hamd) after the Imam says "Allah hears those who praise Him" (Sami'a Allahu li man hamidah). Some scholars are of the view that the congregant should combine both.