Is it possible to apply the Prophetic Sunnah in determining the times of Iftar (breaking fast) and Suhoor (pre-dawn meal), or must astronomical calculations be followed, especially with the clear signs of sunset and the appearance of true dawn?

Allah made the beginning of abstention (Imsak) at the rise of true dawn (Fajr As-Sadiq). So, whoever has not discerned the dawn, may eat until he is certain of its rise, because the default is the continuation of night. As for breaking the fast (Iftar), it is at the disappearance of the sun. So, whoever is certain of its setting is permitted to break his fast. If the signs of the sun's setting and the appearance of true dawn are clear and you are knowledgeable about them, you may rely on them without being restricted by the calendar.