Is it obligatory to interrupt the prayer and start anew when in doubt about a specific nullifier, and does this open the door to [religious] whisperings (waswasah)?

It is not permissible for a responsible individual (mukallaf) to undertake an action until he knows Allah’s ruling concerning it. He must ask scholars and follow those who are followed. So, whoever doubts whether an action performed during prayer invalidates it or not, his prayer is valid, because the default is its validity until its invalidity is proven with certainty. Anything that is doubted is disregarded in Sharia (definition). Thus, if one doubts a divorce, it does not result in the annulment of the marital bond; rather, the existing state is presumed.