What is the ruling regarding my prayer if I find a small trace of impurity on my clothes after passing wind, and I prayed knowing about it? And am I required to check for the presence of impurity before every prayer? And must I repeat the missed prayers?

The impurity that exits from the anus is not among those for which a small amount is pardoned. It must be washed off the garment, and its trace must be removed from the body by performing istinja' (ritual cleansing after defecation or urination). Prayer is not permissible in its presence, because removing impurity is one of the conditions for the validity of prayer according to the majority of scholars. There is no need to search for impurity, but if its presence is known, then istinja' and washing the garment become obligatory. It is more prudent to make up the past prayers that were performed in this manner.