Is it permissible to do what the Prophet, may Allah bless him and grant him peace, did, such as calling the Adhan and performing the Fajr prayer in congregation upon waking up late, by analogy with the story of Bilal, or is that restricted to travel, and must it be made up if we are not traveling?

Every prayer must be performed at its legally prescribed time, and it is not permissible to delay it except for an excuse. If a prayer is missed due to an excuse, there is no blame, and the Muslim must strive to perform it on time. Jurists have differed regarding the ruling on the adhan (call to prayer) and iqamah (call to commence prayer) for a missed prayer. The majority of scholars hold that it is legislated to make the adhan and iqamah when making up a missed prayer, citing the hadith of Abu Qatadah when they overslept and Bilal made the adhan and iqamah, and the hadith of the Battle of the Trench when the Prophet delayed prayers and then made the adhan and iqamah for each prayer. There is no difference in this regard between being resident or traveling. The adhan and iqamah are recommended for a missed prayer, but if one suffices with only the iqamah, there is no blame on him. If one makes the adhan, it is preferable to do so discreetly and not audibly.