Is it permissible to make up for missed regular and recommended Sunnah prayers due to a valid excuse, as well as to make up for missed Qiyam al-Layl (night vigil prayer) and Witr?

The scholars have differed regarding Qiyam al-Layl (night prayer). Some hold that it is achieved by performing any prayer at night, even if it is making up missed obligatory prayers or supererogatory ones. However, the most sound opinion is that night prayer is intended in itself, and it is the best and most rewarded of supererogatory prayers. It is not replaced by regular Sunnah prayers or the like, and it is not permissible to combine it with regular Sunnah prayers with a single intention, because each of them is intended in itself.

The rule regarding the overlapping of acts of worship is that Sunnah acts that are intended in themselves do not overlap, unlike those whose purpose is merely the action itself. So, if an act of worship is intended in itself, or is subsidiary to another, then they cannot overlap. However, if the purpose is merely the action, and the worship itself is not intended (in itself), then acts of worship can overlap.

Based on this, it is not permissible to combine making up Sunnah prayers and Qiyam al-Layl with a single intention. You either make up the Sunnah prayers or you pray Qiyam al-Layl. It is important to note the seriousness of neglecting to perform obligatory prayers within their prescribed times.