Are a doctor's appointment, obtaining official documents, attending to personal and family matters, studying, working, or a sick mother's needs considered valid excuses for missing congregational prayers in the mosque or elsewhere?

Whoever prays the fard (obligatory) prayer in congregation outside the mosque has fulfilled what is incumbent upon him. There are excuses that permit one to miss Jumu'ah (Friday prayer) and congregational prayers, such as unbearable hardship due to illness or fear. Thus, your presence at the doctor for an examination when your turn has come, or your going for study or work, or obtaining government documents, or nursing your mother—all of these are considered valid excuses that permit you to miss congregational prayer in the mosque. However, one should be keen to perform prayer in congregation in the mosque and not use excuses that can be postponed.