Is the fatwa stating that the Fajr adhan should be advanced by 20 minutes correct, and should it be followed, or should the timing set by the ruler be followed, knowing that some people delay the two rak'ahs of Fajr until after the obligatory prayer based on this?

Calendars approved by trustworthy scholars are to be acted upon, unless they contradict the Sharia signs. As for unknown calendars, they can be used for approximation but not relied upon entirely. If a calendar is in use and approved by trustworthy scholars, doubts should be disregarded unless the one raising doubts is a person of knowledge, in which case verification is necessary. If a calendar is not approved by scholars or its source is unknown, it should not be relied upon. When in doubt about its accuracy, the time of Fajr should be investigated, because the prayer time does not enter with doubt but rather with certainty or strong probability.