What should an expatriate do about the difference in prayer times between mosques in India? Is it permissible for him not to listen to the Friday sermon if it contains innovations (bid'ah)? And how should he advise his friends to abandon invoking saints and visiting graves?

Prayer times are known by the শরعي signs. If you cannot determine them yourself, then follow those who are trustworthy. Praying at the beginning of the time in one mosque and then in another does not harm, as long as it is within the time. Attending Friday prayer is obligatory upon hearing the call, even if the preacher resorts to a non-disbelieving innovation. However, seeking intercession through the status of awliya' (saints) is an innovation. To advise friends, gift them books that address the topic of intercession if you are not qualified to debate.