What is the ruling on the prayer of one who prayed while a wound in his mouth was bleeding and had not completely stopped? And is placing a handkerchief with traces of impurity in one's pocket considered a mistake? And is it permissible to pray with the congregation in this situation?

There is no harm in praying with a small amount of blood, nor in carrying a handkerchief stained with it. A small amount of blood is excused in prayer because it is difficult to guard against, and it does not invalidate the prayer. This is the opinion of a group of Companions and Tabi'in. As for a large amount of blood, it is not excused except when one is unable to remove it, for avoiding impurities is a condition for the validity of prayer, provided one has knowledge and ability.