Q 3: We cannot hear the Adhan (call to Prayer) because the Masjid (mosque) is far away from the place where we live.
Is it permissible for us to break our Sawm (Fast) once we see that the sun has set?
When you are most certain that the sun has already set or you think it has most likely set, as you are not positively sure of its setting, (Part No. 9; Page No. 32) due to heavy clouds, then you may break your Sawm even if you are too far away from the Masjid to hear the Adhan. This is based on a Hadith in which the Prophet Muhammad (peace be upon him) is reported to have said:
When night falls from this side and the day disappears from this side and the sun has sets, then the fasting person should break fast.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.