What is one's duty regarding the issues raised concerning prayer times in Amman, and when should one pray, taking into account the difficulty of observing the times?

The default rule is that prayer is not permissible unless one is certain of the entry of its time, or has a strong presumption of it. It is permissible to eat and drink until the dawn becomes clear, and it is not permissible to break the fast until one is certain of sunset or has a strong presumption of it. Due to the difficulty of knowing the time of dawn by natural signs in cities, Muslims rely on calendars. If one doubts the entry of a prayer's time, they should investigate and pray after being certain, especially regarding Fajr prayer, as there has been a difference between calendars and the actual sighting of dawn. Therefore, it is preferable to delay the prayer slightly as a precaution. As for 'Isha prayer, delaying it is minor and causes no harm. When there is a difference between two calendars, we prioritize the later one for all times, because the default is that the time has not yet entered, and it is permissible to follow the opinion of whoever says "the time has not entered" until they agree.