How can one ensure the accuracy of prayer times, especially Fajr and Maghrib, in Michigan, USA, given the doubt regarding the validity of the announced times, which do not align with the signs in the sky?

If there is an Islamic center in your city, then you should pray and fast according to their timings. If there is no Islamic center and you cannot determine the time yourself, then we advise you to act according to one of the timetables provided by the Muslim World League, Al-Azhar, or others.