Is it permissible to follow the prayer times of Sunni mosques, or should the prayer times of the people of innovation be observed—who combine Dhuhr and Asr, and Maghrib and Isha—when you reside in their city?

The basic principle for determining prayer times is based on the legal signs, not written calendars. It is permissible to rely on calendars issued by trustworthy sources. However, those who follow innovations (bid'ah) are not to be trusted in this regard, especially those whose innovations amount to disbelief (bid'ah mukaffirah). If it is difficult to determine the times oneself, then one must rely on the calendars of Ahlus-Sunnah. In case of a discrepancy, the later time for the entry of the prayer is to be adopted.