What should one do who has prayed Fajr alone and then heard the call to prayer (iqamah) in the mosque; should he go to the mosque or not?

When you wake up, do not tell yourself that you are late. Rather, confirm the time by looking at the clock or at the dawn. If it becomes clear that people have already prayed, there is no harm in you praying at home. However, if they have not prayed, then you must go out to pray with the congregation, because it is obligatory for a man who has no valid excuse to pray in congregation.