Must the prayer be repeated if four spots of feces, the size of a dirham, were found in the underwear, which was wet with water used for Istinja' (washing after defecation or urination), after the Maghrib prayer? And does the moisture in the underwear and the chair that was sat upon become impure due to this forgivable impurity? What is the ruling on the purity of the chair in this case?

The traces of feces are an impurity that is not excused. The spot on clothing stained with feces is considered impure, and the impurity must be removed from it for prayer, whether it is wet or dry. The default is that impurity does not transfer to the sitting area, and its transfer is not confirmed by doubt, but only by certainty. If the excretion of fecal droplets after prayer is probable, they are attributed to the time after prayer, and your prayer is valid. If you were certain they exited before prayer, and you performed ablution afterwards, and you were unaware of their presence and did not remove them, then your prayer is valid, because avoiding impurity is a condition when there is knowledge and ability. However, if they exited before prayer after ablution, then it is obligatory to repeat the prayer because it was performed without purification. If you suffer from obsessive doubts, ignore them and turn away from them.