Is it permissible to return a greeting verbally while reciting the Quran, or by gesturing, and should the recitation be resumed with the Basmalah after returning the greeting?

Initiating the greeting (salām) is a confirmed Sunnah, and returning it is an individual obligation (fardh 'ayn) for one person, and a communal obligation (fardh kifāyah) for a group. The reciter is like anyone else who is greeted and is expected to return the greeting. It is commendable for someone who passes by a reciter to greet them, and the reciter is obliged to return the greeting verbally, not by gesturing. If the reciter returns the greeting, it is commendable for them to repeat the Isti'ādhah (seeking refuge with Allah), but if they do not, there is no sin. As for the Basmalah (reciting "Bismillah"), the reciter has a choice regarding it when resuming recitation or responding, except at the beginning of chapters, where it is obligatory.