What should I do about my doubt concerning the validity of my previous prayers, especially Fajr and Dhuhr, due to the delayed Adhan compared to the prayer's entry time according to the calendar?

Acting upon reliable calendars, such as the Umm al-Qura calendar, is valid and discharges one's duty. Doubts about an act of worship after its completion do not affect its validity.

Therefore, there is no need to repeat past prayers if they were performed according to an approved calendar, and no attention should be paid to doubts arising after the completion of the prayer.

It is permissible to delay the prayer until the end of its time, as long as it does not go beyond that time.