What should one do if he misses Fajr Prayer in congregation in his residence? Should he ask one of his friends to pray a supererogatory prayer with him, or should he pray alone immediately? And would he be sinful if he does not find anyone to pray with him?

If you wake up after the congregational prayer has finished, you must pray immediately after purification. It is better to pray in congregation if you find someone to pray with you, but you are not obligated to ask anyone to do so. Congregational prayer is obligatory according to the most authoritative opinion, but it is not an individual obligation (fard ayn) according to the majority of scholars. A person who sleeps before the prayer time enters is not sinful.