Should one make up prayers that were performed quickly and without ṭuma’nīnah (tranquility/composure) or with a distracted mind, or prayers that were performed at home despite knowing the obligation to pray in the mosque?

If you performed prayers without ṭuma’nīnah (tranquility/stillness) and did not fulfill its obligatory minimum, then your prayer is invalid and must be repeated according to the majority of scholars. However, if you fulfilled the obligatory minimum but omitted the recommended ṭuma’nīnah, then you are not required to repeat the prayer. If you do not know the number of prayers that must be repeated, then strive to determine it through investigation (taḥarri) and make up what you believe, with a strong presumption, clears your responsibility. As for khushūʿ (devotional humility), it is the essence and spirit of prayer; you must strive to attain it, but do not repeat the prayer due to its absence. Congregational prayer in the mosque is obligatory according to a group of scholars and recommended according to others, which is the opinion acted upon in fatwas.